Inference: Tevilah is required, but not ha'Erev Shemesh. This is like we infer below (23a) about Kelim that are finished.

Support #1: In Zevachim (99a), we infer about this Mishnah "what is the case? If [an Onen] diverted his mind from [guarding himself from] Tum'as Sheretz, (perhaps he touched one, and) he is totally Tamei. He needs ha'Erev Shemesh! (This shows that really, an Onen does not require ha'Erev Shemesh.)

Support #2: Also Rashi explained there that he does not require ha'Erev Shemesh.

Implied question: A Mishnah says that a Tevul Yom and Mechusar Kipurim do not receive a share of Kodshim to eat them at night.

Inference: A Mechusar Kipurim requires ha'Erev Shemesh. (Therefore, there was no Hava Amina that he may eat during the day. We needed to teach only that he does not receive to eat at night.)

Answer: We can say that it says [at night] due to a Tevul Yom.

Question (Ri): It says in Eruvin (32a) that if a woman was obligated [to bring a Korban for] a birth or Zivah, she brings coins, and puts them in the box [for this. Kohanim buy birds with the money and offer them.] She immerses and may eat Kodshim at night.

There it does not mention a Tevul Yom [with her, so we cannot answer like above]!

Answer: It mentions at night, for she does not stand there while they offer [the birds]. She relies on the Chazakah of Beis Din, and eats at night. The Chazakah is that Beis Din is not lazy.

Question: She should be permitted after midday, for we find regarding the Omer (Menachos 68a) that people far [from the Mikdash] are permitted [to eat Chodosh] from midday and onwards, because Beis Din is not lazy! (Surely, they offered it before midday.)

Answer: We can distinguish. There, for a Korban Tzibur, they rush more, to do it before midday. Regarding a Korban Yachid, they delay the entire day, but no longer, so people will not stumble through them.

Question: It should be permitted after the afternoon Tamid, for after this we need not wait, for it says "Aleha" regarding Olah, from which we learn the Aseh of Hashlamah, that we may not offer anything after the afternoon Tamid!

Answer #1: We can say that sometimes they delay the [afternoon] Tamid until evening, like we say in Berachos (26b) that one may offer it until evening;

Therefore, since there is no fixed time, we have a total Safek (until the last possible time).

Answer #2: This is like R. Yishmael, son of R. Yochanan ben Brokah, who says (Pesachim 59a) that Chatas ha'Of may be offered after the afternoon Tamid. (R. Akiva Eiger asks that R. Yochanan agrees that mid'Rabanan it is forbidden, if not to enable eating Kodshim (e.g. Pesach. Here, the Kohanim do not know that she plans to eat Kodshim tonight.) Rather, one may offer even after Zerikas Dam ha'Tamid, as long as it is before the limbs are burned, which may be after dark.)

Support #1 (for answer (g)): The Ri explains like this in Pesachim regarding a Mechusar Kipurim, who immerses and eats Kodshim at night;

It did not mention "at night" due to ha'Erev Shemesh, rather, because he does not stand there while they offer his Korban, like I explained. He relies on the Chazakah of Kohanim.

Support #2: We can explain like this also in Kerisus (8b) regarding a convert, who may not eat Kodshim until he brings his Kan (two birds). If he brought one bird in the morning, he may eat Kodshim at night. It says so for a bigger Chidush;

Even though he brought it (his Kan) in the morning, i.e. both [birds], he may not eat until the evening when he relies on the Chazakah, like I explained.

You cannot say that there [he must wait until evening] for ha'Erev Shemesh, for it is not needed, like I explained.

Also, it does not mention Tevilah there. Also, we find that Mechusar Kipurim requires Tevilah only regarding Mechusar Kipurim of Tum'ah, but not for a convert.

Support #3 (for Inference (a)): A Mishnah (Parah 11:5) says that anyone who needs Tevilah mid'Rabanan is Metamei Kodesh... after Tevilah he is permitted all of them.

Inference: Whenever [the need for Tevilah is only] mid'Rabanan, he is permitted immediately without ha'Erev Shemesh.

Support #1 (for Support #3): Based on this explanation, R. Shmuel of Ra'us answered the Beraisa in Beitzah (18a) [taught in the Tosefta] regarding the Mishnah (17b);

Citation (18a - Beraisa): If a Kli was Nitma through a Vlad ha'Tum'ah, we may immerse it on Yom Tov.

Question: Why is this permitted? It needs ha'Erev Shemesh [before one may use it for Taharos. The Tevilah is not for the sake of Yom Tov!]

Answer (R. Shmuel): Since [it was Nitma through] a Vlad ha'Tum'ah mid'Rabanan, it does not require Ha'Erev Shemesh.

Support #2: The Yerushalmi in Terumos, in the Gemara about immersing Kelim on Shabbos, it says "if his Kli fell into a pit, he schemes and immerses it", i.e. on Yom Tov;

Regarding Shabbos, two Amora'im argued. One said that [it is permitted even for] a Kli Nitma through an Av ha'Tum'ah, and one said [only for] a Kli Nitma through a Vlad ha'Tum'ah.

The one who said that it was Nitma through a Vlad ha'Tum'ah asked against the one who said it was Nitma through an Av ha'Tum'ah, even during the week it requires ha'Erev Shemesh!

Explanation: Granted, I say [that it was Nitma through] a Vlad ha'Tum'ah. It is fine that it does not require ha'Erev Shemesh.

However, you say [that it was Nitma through] an Av ha'Tum'ah. It should require ha'Erev Shemesh, and it cannot be used only on a Yom Chol (Motza'ei Shabbos)! If so, he immerses on Shabbos for the sake of Chol!

We establish that he wants to use it for Chulin. A Tevul Yom is permitted Chulin without ha'Erev Shemesh.

Conclusion: According to his opinion, we establish the Beraisa in Beitzah (18a) "we may not immerse [on Yom Tov] Kelim that became Tamei through an Av ha'Tum'ah" to discuss a Kohen who wants to eat Terumah, or one who eats Chulin Al Taharas Terumah;

He permits a Tum'ah mid'Rabanan (through a Vlad ha'Tum'ah) only through scheming. (Maharsha - i.e. according to the opinion that permits a Vlad ha'Tum'ah).

Also the Sugya in Beitzah discusses through scheming, and if it became Tamei through an Av ha'Tum'ah, even through scheming it is not [permitted].

Implied question: Why does a Beraisa there permit to draw water with a Tamei bucket, and [since it gets totally submerged] automatically it is Tahor?

Answer: That scheme is better (the bucket comes up full of water. It looks like he intended for an action other than Tevilah) than if he returned it empty.

That text is brought properly in the Yerushalmi [in Terumos], and it is also in [the Yerushalmi] in Beitzah, [but there] it is written in Seforim with mistakes. However, the explanation of the text is like I explained.

Support #4 (for Inference (a) - (Ri)): In Pesachim (90b) Rav taught that we do not do Shechitah [of Korban Pesach] and Zerikah for one who is Tamei due to a Sheretz, lest he be negligent and not immerse;

Regarding a Mechusar Kipurim, it says there that we do Shechitah and Zerikah for him. We are not concerned lest he be negligent;

Since mid'Oraisa he is properly Tahor, Chachamim did not enforce their words to exempt him from Pesach in a situation of Kares [i.e. for one who intentionally neglects to offer it]. We properly slaughter and do Zerikah for him. (Maharsha says that our Tosfos is missing words. In Zevachim (98b DH Tevul), Tosfos explained that if one touched a Sheretz, we are concerned lest he not immerse until night, and then he cannot eat Pesach because he needs ha'Erev Shemesh. There is no concern for Mechusar Kipurim, even if he immerses at night, for he does not need ha'Erev Shemesh. The Ri rejects this proof. We are lenient about Mechusar Kipurim because mid'Oraisa he does not need Tevilah!)

Implied question: It says in Yoma (47a) that R. Yishmael ben Kimchis Kohen Gadol was talking with a Nochri in the market [on Yom Kipur], and spit left the Nochri's mouth [and landed on R. Yishmael], and his brother served in place of him.

He should have immersed [and served]! Since the Tum'ah [of live Nochrim] is mid'Rabanan, he does not require ha'Erev Shemesh!

Answer: There, we can say that since Chachamim made Nochrim like Zavim in every way, they were stringent and obligated ha'Erev Shemesh.

Observation: Regarding spit of an Am ha'Aretz, the Sugya below (23a) of a tube connotes that it obligates ha'Erev Shemesh.

Citation (23a) Question: [If an Am ha'Aretz cut it for the sake of Parah Adumah,] why must we be Metamei it and immerse it [to show that a Tevul Yom is Kosher for Parah]? It is already Tamei!

Question: What was the question? The initial Tum'ah does not require ha'Erev Shemesh, and there is no Heker (recognition);

If we are Metamei it, it requires ha'Erev Shemesh, and there is Heker unlike the Tzedukim!

Answer: Rather, surely even spit of an Am ha'Aretz obligates ha'Erev Shemesh.

Support: A Mishnah (Parah 3:7) says that they were Metamei the Kohen who burns the Parah;

A Beraisa in the Tosefta says that they would touch him, like I explained above, that garments of those who eat Kodesh are Midras regarding Chatas (Parah Adumah).

Question: What is the Heker unlike the Tzedukim? It does not require ha'Erev Shemesh, like I explained!

Answer (R. Shimon): They made him like a Tamei Mes on his seventh day, like below (23a, regarding the tube). Therefore, he needs even ha'Erev Shemesh.

Question: However, Rashi explained unlike this below. Rather, he explained that they made it like a Tamei Mes on his seventh day to count Rishon and Sheni [for foods that it is Metamei], but not regarding ha'Erev Shemesh. (Maharsha - we said so about the Hava Amina "we made it like a Tamei Sheretz"! We conclude that they made it like a Tamei Mes on his seventh day to be Metamei people, like Rashi explained there. In any case, it requires ha'Erev Shemesh. If not, there would be no Heker unlike the Tzedukim!)

This is difficult, for now it connotes that there is ha'Erev Shemesh even for Tum'ah mid'Rabanan, whereas in the Mishnah of "everyone who requires Tevilah" connotes that there is no ha'Erev Shemesh!

Answer (Ri): The case of being Metamei the Kohen who burns the Parah discusses in order that he will be Tamei to be Metamei Chulin through touching;

The same applies to the case of spit of an Am ha'Aretz and spit of a Nochri that spewed from his mouth. He is Metamei Chulin through touching. Therefore, they require ha'Erev Shemesh.

Rebuttal: However, the words connote that he is not Metamei Chulin through touching in the case of the Kohen who burns the Parah;

Also below (23a), regarding the tube, it says that they made it like a Tamei Mes on his seventh day only regarding ha'Erev Shemesh, but not to be Metamei Chulin through touching!

Implied question: [If so] why does he require ha'Erev Shemesh?

Answer: Chachamim were stringent about Parah. (I.e. for other matters he needs ha'Erev Shemesh, so there will be a Heker that a Tevul Yom is Kosher for Parah - PF.)

Also, they were stringent about a tube (23a) more than [the usual decree] about Kelim that are finished, for which Tevilah suffices without ha'Erev Shemesh. This is for Chulin, Terumah (indeed, these two do not require even Tevilah) and Kodesh, but not for Chatas.

Implied question: In Pesachim (70a), it says that if a knife was found on the 13th [of Nisan], one immerses it again. If it was found on the 14th, one may slaughter with it immediately;

Presumably they immersed it yesterday, so it will have ha'Erev Shemesh [before it is needed for Korban Pesach].

We should be concerned lest it became Tamei mid'Rabanan, which does not require ha'Erev Shemesh, and the owner delayed immersing it until the morning [of the 14th, and he lost it before immersing it]!

Answer #1: This is a Safek about [a Tum'ah] mid'Rabanan. We are lenient.

Answer #2: It is normal to immerse from the night before, lest one be so distracted (the next day) that he not immerse it.

Question: Where was the knife found? If it was in Yerushalayim, even on the 13th [we may assume that it is Tahor]. If it was outside Yerushalayim, even on the 14th we may not [assume that it is Tahor], like it says in Pesachim (19b)!

Answer: We can say that it was found outside Yerushalayim, or in Yerushalayim, in small alleys not on the descent or ascent [to the Mikveh. It is a Safek whether it fell on the descent to the Mikveh, or on the ascent.]

On the 14th, there is a proof that it was immersed, so it is permitted.

Question (R. Eliyahu): The knife should be disqualified due to Hesech ha'Da'as, like it says above (20a)!

If one said "I was mindful of the basket, but not of the shovel, we disqualify it due to Hesech ha'Da'as!

Answer (Ri): Hesech ha'Da'as disqualifies only in a case like there, when it was b'Yado (within his control), and he diverted his mind from it;

However, when it is not b'Yado, e.g. he lost it, Hesech ha'Da'as does not apply to disqualify.

Support (R. Elchanan): In Shekalim (7:3), the Mishnah says that if limbs were found in the Azarah, they are [assumed to be] of Olos. Pieces are of Chata'os;

It connotes that we offer the Olah limbs and eat the Chatas. It is not Pasul due to Hesech ha'Da'as. (R. Akiva Eiger - the Mishnah explicitly says that we leave the limbs and pieces to become Nosar! Rashash - one opinion in the Yerushalmi says that this is because perhaps they are already Nosar [but not due to Hesech ha'Da'as].)

Question (R. Elchanan): Why does it say "one immerses it again?" This connotes it was already immersed!

Answer (Ri): Even if he recognizes that the owner immersed it, he immerses it [again]. Perhaps it says there was not guarded in Taharah, since there is a delay the entire day. (If it becomes Tamei on the 13th after Tevilah, he can immerse it again, and it will be ready to use on the 14th.)

Rebuttal (of answer (j:3:ii of R. Shmuel) - R. Elchanan): In the Sugya in Beitzah, we say that a Kli Nitma through a Vlad ha'Tum'ah, we may immerse it on Yom Tov. [Tosfos] asked that it needs ha'Erev Shemesh. That refers to Yom Tov that fell on Erev Shabbos.

Yom Tov prepares for Shabbos. Therefore, we immerse it even for another day (Shabbos).

Rejection (of Rebuttal): The words connote unlike this. Rather, it discusses every Yom Tov. (We must answer like R. Shmuel above, who derived from this that a Kli Nitma through a Vlad ha'Tum'ah does not require ha'Erev Shemesh.)

Explanation #1: The Mishnah says that one must dry [the Kli] due to Chatzitzah, like Rashi explained.

Implied question: Why didn't he explain why it was needed to teach also drying?

Answer: He knew that we cannot learn it from the others.

Explanation #2: Some say that there is a different reason for drying, because the water returns and is Metamei [the Kli]. It is a stringency of Kodesh that Hashakah (connection to a Mikveh) is not Metaher the water.

Question (my Rebbi): If so, [this is an independent stringency unrelated to untying, so] according to Rava there are 11 stringencies, and according to R. Ila there are 10!

Answer: They do not count a Revi'i [l'Tum'ah] or Tziruf, which is mid'Oraisa. (They count only stringencies mid'Rabanan.)

Question (R. Elchanan): Rav Mari proved above (19b) that Chulin processed Al Taharas ha'Kodesh are like Kodesh, since we did not teach [the following] among the stringencies;

I.e. garments of those who eat Terumah are Midras to Chulin Al Taharas ha'Kodesh. Garments of those who eat Chulin Al Taharas ha'Kodesh are Midras to Kodesh.

Summation of question: What is the proof? Perhaps for other matters, they (Chulin Al Taharas ha'Kodesh) are not like Kodesh, but for this stringency, they are like Kodesh!

We find that our Mishnah holds that regarding the first five stringencies, they are like Kodesh, and even so they are not listed among stringencies (it did not teach that they apply even to Chulin Al Taharas ha'Kodesh)!

Answer: Perhaps the Gemara said [that Chulin Al Taharas ha'Kodesh are like Kodesh] only regarding this stringency (that Bigdei Ochlei Terumah are Midras to Kodesh).

Question #1 (Ri): We say in Nidah (6a) that me'Es la'Es of Nidah (she is retroactively Tamei 24 hours before she sees blood) applies to Kodesh, but not to Terumah;

Citation (6a) Question: If so, it should be listed among stringencies [of Kodesh]!

Citation (cont.) Answer: We taught only matters in which there is Derara (grounds for concern) [for Tum'ah mid'Oraisa], but not matters in which there is no Derara of Tum'ah mid'Oraisa.

What was the answer? Regarding the latter stringencies, we count [matters with] Derara of Tum'ah mid'Rabanan, and that (me'Es la'Es of Nidah) is Derara of Tum'ah mid'Rabanan!

Question #2: What is different about the latter matters, which do not apply to Chulin Al Taharas ha'Kodesh? There we conclude that me'Es la'Es applies even to Chulin Al Taharas ha'Kodesh [even though there is Derara only of Tum'ah mid'Rabanan]!

Answer #1 (Riva): There, we ask that it should be listed among the stringencies only from the first matters;

Regarding the latter, they are not similar. There (me'Es la'Es of Nidah) is even for Chulin Al Taharas ha'Kodesh, but here (the latter stringencies) are only for Kodesh.

Objection #1 (Ri): The Gemara did not yet know this (that it is even for Chulin Al Taharas ha'Kodesh) when it asked (why me'Es la'Es was not taught), until the conclusion there.

Objection #2: When we answer that it is unlike the first matters, for it has no Derara of Tum'ah, still we can ask why there, it is for Chulin Al Taharas ha'Kodesh, and here, it is only for Kodesh!

Answer #2 (Ri): [There, we asked that] it should be listed among the stringencies, either among the first matters or the latter matters;

We answer that there is no Derara of Tum'ah at all, even mid'Rabanan, so it is unlike even the latter matters.

When we are Metamei her [retroactively] me'Es la'Es, we know that she was Tehorah.

Implied question: How do we conclude there that it is even for Chulin, since there is no Derara of Tum'ah at all?

Answer: It is somewhat normal that the blood is uprooted [from its source] before she sees it. Therefore, Rabanan decreed even for Chulin Al Taharas ha'Kodesh.

In any case, there is no Derara of Tum'ah there, since when she engaged with the Taharos, there was no Safek Tum'ah;

She should not refrain from engaging with Taharos just because she does not know when she will see afterwards.

Question (Ri): The Mishnah taught a Revi'i (l'Tum'ah) in Kodesh and a Shelishi in Terumah, which are mid'Oraisa, like it says in Sotah (29a)!

Reference: I will explain this below (23b DH v'Ha, 24a DH Minayin), with Hash-m's help.

This is unlike Rashi, who said that a Revi'i in Kodesh is mid'Rabanan.

Question (my Rebbi): Rav Nachman said in the name of Rabah bar Avuha that we listed 11 stringencies. The first [are even for Chulin Al Taharas ha'Kodesh]; the last are only for Kodesh;

If so, he holds that all the latter matters have no Derara of Tum'ah d'Oraisa;

Below (24a), we hear that he holds that Tziruf of a basket is mid'Oraisa, for he answers the teaching of R. Chanin "the case is, he piled it on a hide. Mid'Oraisa, something with an interior joins [its contents]."

Inference: He holds that [Tziruf] is Mid'Oraisa in a Kli with an interior!

Answer (Ri): Since it does not apply to Chulin, it is not considered Derara of Tum'ah, i.e. association with Tum'ah.

Explanation #1 (Rashi): [This is the width of] two fingers [rotating and] returning to their place.

Question (R. Tam): A Mishnah (Taharos 9,8) brought in Gitin (16a) and Avodah Zarah (72a) says that Nitzuk, Ketafres (a liquid poured through the air or flowing down an incline), or a liquid Tofe'ach (it wets what touches it), are not connections;

Inference: Tofe'ach Al Menas Lehatfi'ach (it wets what touches it, enough to wet something else) is connected! (Why do we require here an opening two fingers wide?)

Answer #1 (and Explanation #2 - R. Tam): It suffices that the water [that goes through it] is Tofe'ach Al Menas Lehatfi'ach, but the hole must be two fingers.

Objection #1 (Ri): A Mishnah in Parah (5:8) says that if there were two stone containers, and one was Mekadesh (put ashes of Parah Adumah on the water in) one of them, the water in the other is not Mekudash;

If there was a hole between them ki'Shfoferes ha'Nod, or water floated on top of them, even the thickness of a garlic peel, if he was Mekadesh one of them, the water in the other is Mekudash.

Inference: Since the Seifa says "or water floated on top of them", this connotes that [when we rely on a hole] in the wall we require ki'Shfoferes ha'Nod even of water.

Only in the Seifa the thickness of a garlic peel suffices.

Objection #2 (Mikva'os 6:9 - Mishnah): If the wall between two Mikva'os was cracked vertically, they join. If it was cracked horizontally, it joins only if in one place there is an opening k'Shfoferes ha'Nod;

Citation (cont.): R. Yehudah says oppositely;

Citation (cont.): If there was a breach between them for a height like [the thickness of] a garlic peel and the width ki'Shfoferes ha'Nod, i.e. two fingers [rotating and] returning to their place [they join].

Inference: Since we require half the hole full of water, there is more than Tofe'ach Al Menas Lehatfi'ach!

Note: This refers to above, when we require an opening k'Shfoferes ha'Nod. Tosfos in Yevamos (15a) explains that if the water coming through the hole is only Tofe'ach Lehatfi'ach, there is not water the width of ki'Shfoferes ha'Nod, for the hole is not square, rather, round. However, there Tosfos says that the hole must be full.

Objection #3: Also, if the Mishnah of Nitzuk and Ketafres was taught regarding Mikva'os, why does it say in Gitin "it is regarding Mikva'os, and it is like R. Yehudah"?

Inference: [Rather,] initially we did not establish it regarding Mikva'os!

Answer #2 (Ri): The Mishnah was taught regarding Hashakah (connecting water to a Mikveh), similar to the Reisha, "a stick full of Tamei liquids, once he did Hashakah to a Mikveh, it is Tahor. R. Yehoshua says so";

Chachamim say, he must immerse all of it. Nitzuk and Ketafres [and a liquid Tofe'ach are not connected]... This is taught at the end of Perek 8 of Taharos.

However, regarding Mikva'os, it (Ketafres) helps, like it says above (19a) about three pools. One may immerse in the bottom one.

When we establish in Gitin "perhaps it is regarding Mikva'os, and it is like R. Yehudah, who says Gud Achis (we project downward)", we could not have established it like Rabanan (since we infer that Tofe'ach Al Menas Lehatfi'ach helps);

They (Rabanan) hold that Tofe'ach Al Menas Lehatfi'ach does not help, even with Gud Achis, and all the more so on level ground. They hold that there is never a connection until there is the thickness of a garlic peel for a width of ki'Shfoferes ha'Nod.

Support: Their words connote like this - "it is never connected..."

Further, we can say also according to R. Yehudah holds that [Tofe'ach Al Menas Lehatfi'ach] helps only when Gud Achis applies, but on level ground we do not say so.

Explanation: Above (19b) I explained that it discusses when there are 40 Sa'im in the middle Mikveh for a bigger Chidush in R. Yehudah. Even though there are 40 Sa'im in the middle, one may not immerse in the top pool;

Alternatively, it is a bigger Chidush in Chachamim. Even so (that there are 40 Sa'im in the middle), in the Seifa of the Tosefta, Chachamim say that one may immerse only in the middle.

Question (R. Elchanan): The reasoning is opposite! Regarding Hashakah, we find that Ketafres is not connected, in the Mishnah of Nitzuk and Ketafres;

Regarding Mikva'os it helps, like it says above regarding three pools. He may immerse in the bottom, for it is connected;

Regarding Tofe'ach Al Menas Lehatfi'ach, it helps for Hashakah, but regarding Mikva'os, we require water floating on top!

Answer (Ri): Tum'ah, Taharah and Hashakah are traditions. They do not depend on reasoning.

Question (R. Elchanan): Regarding Tofe'ach Al Menas Lehatfi'ach, it is connected regarding Hashakah, but regarding Mikva'os, we require water floating on top;

When we say "perhaps it is regarding Mikva'os", this means that for Hashakah it is not connected!

Answer: The same applies to Hashakah. (Even if we establish the Mishnah to discuss Mikva'os, Tofe'ach Al Menas Lehatfi'ach is connected also for Hashakah.) When one can say Gud Achis, it is connected according to R. Yehudah.

Implied question: Why does it discuss Mikva'os? (It should have taught this regarding Hashakah. This is a bigger Chidush, for we are more stringent about Hashakah regarding Ketafres!)

Answer: This is because we were discussing Mikva'os.

Explanation #3: We can distinguish from the beginning and resolve all of the Mishnayos. On level ground, when there is no wall at all, Tofe'ach Al Menas Lehatfi'ach suffices;

When there is a hole in the wall, we require the width of ki'Shfoferes ha'Nod;

On top of a wall, the thickness of a garlic peel suffices, for the width of ki'Shfoferes ha'Nod. (See Tosfos Yevamos 15a DH Eruv.)