Rashi's opinion: There is a Hekesh between Sereifah and Hotza'ah.

Question: In Kodshim, something learned from a Hekesh cannot teach through a Hekesh!

Since Hotza'ah itself is learned from a Hekesh, since skin and meat are Hukash to Peresh (excrement), how can we learn Sereifah from it through a Hekesh?

Suggestion: Since they are burned outside of three Machanos, their skin and meat are not considered Kodesh regarding this, that they should not be able to teach through a Hekesh. Rather, they can teach through a Hekesh.

Rejection: In Zevachim (50a), we bring this Beraisa, and learn from it that something learned from a Gezeirah Shavah can teach through a Gezeirah Shavah in Kodshim!

Answer: We can say that Sereifah [of the meat] itself is Hukash to Peresh. Just like the Peresh is inside at the time of Sereifah, also the meat is in the skin;

"V'Saraf" applies to its skin, meat, head, feet, innards and Peresh. He burns all of them. Just like the Peresh is inside, for it would be disgraceful to burn the Peresh by itself, also the meat is in the skin;

Defense: However, I can resolve Rashi's opinion. (Si'ach Yitzchak - the Limud from Hotza'ah is not a Hekesh, rather, a Giluy Milsa. Just like the meat is in the skin at the time of Hotza'ah, also at the time of Sereifah.)

Question #1: What is the source for three Machanos for Par ha'Edah (Helam Davar)?

Suggestion: We learn from Par Kohen Mashi'ach.

Rejection: We learn Par Kohen Mashi'ach from a Hekesh from ashes. Something learned from a Hekesh cannot teach through a Hekesh!

Answer #1: According to the opinion that something learned from a Hekesh and something else is not considered a Hekesh (so it can teach through a Hekesh), this is fine;

Since we learn from it (Par Kohen Mashi'ach) the Machaneh written regarding it, we learn from it also the Machaneh we learned for it from a Hekesh.

Question #2: In Sanhedrin (42b), we learn that the Mekalel (blasphemer) was stoned outside of three Machanos from a Gezeirah Shavah to Parim ha'Nisrafim.

Something learned from a Hekesh cannot teach through a Gezeirah Shavah!

This is difficult according to the opinion in Zevachim that it depends on the source. (If the source is Kodshim, we may not learn), even if the Nilmad (what is learned) is Chulin.

Question #3: In our Sugya, we say "there you give three Machanos, and here [only] one Machaneh! I.e. we learn them from each other through a Gezeirah Shavah Chatas-Chatas in Zevachim 83a.

Something learned from a Hekesh cannot teach through a Gezeirah Shavah!

Question #4: R. Shimon learns Parah [Adumah] from Par Yom Kipur, that it is outside of three Machanos. Par Yom Kipur itself we know through a Hekesh from Par Kohen Mashi'ach, like Rashi explained!

We expound "Par" to be Par Yom Kipur, which is Hukash in the verse to Par Kohen Mashi'ach and Par Helam.

Another verse says "v'Es Par ha'Chatas v'Es Se'ir ha'Chatas." The word ha'Chatas is repeated to teach about other Korbanos that are burned. They are Hukash to each other.

All the more so this is difficult! Here he learns Parah from a Gezeirah Shavah from Par Yom Kipur, and Par Yom Kipur from a Hekesh from Par Kohen Mashi'ach, which itself was learned from a Hekesh!

Granted, regarding to the east of Yerushalayim, he learns Yom Kipur from Parah. He can then learn from it Par Kohen Mashi'ach, according to Rav Papa in Zevachim, who says that it depends on the source;

The source is Chulin, for Parah is Kodshei Bedek ha'Bayis.

However, how can Yom Kipur teach about Parah? The source is Kodesh!

Answer: We do not learn Par Yom Kipur and Par Kohen Mashi'ach from each other through a Hekesh;

Rather, we learn through a Gezeirah Shavah "Ohr, Basar and Peresh", like above, or through a Gezeirah Shavah "ha'Chatas-ha'Chatas." It says "ha'Chatas" regarding all of them.

This is unlike Rashi said, that it is a Hekesh.

Now it is not difficult. This is something learned from a Gezeirah Shavah, which can teach through another Gezeirah Shavah.

Answer #2 (to Question #1): Also Par Helam Davar, according to the opinion that something learned from a Hekesh and something else is considered a Hekesh, is not learned from a Hekesh, rather, from a Gezeirah Shavah "ha'Chatas-ha'Chatas."

Note: The Maharsha does not understand how this helps. One Machaneh of Par Kohen Mashi'ach was learned from Terumas ha'Deshen through a Hekesh. It cannot teach to Par Helam Davar through a Gezeirah Shavah!

Even according to R. Meir, who says in Zevachim that we do not need the Drashah "Chatas", for it says Lechaper..., this is not because he does not learn the Gezeirah Shavah;

Rather, he means that we do not need the Gezeirah Shavah for Tum'as Begadim, for we learn it from "Lechaper".

Alternatively, he learns burning outside of three Machanos from a Gezeirah Shavah "mi'Chutz la'Machaneh", like R. Shimon.

Question: Why does R. Shimon need to expound an extra "mi'Chutz la'Machaneh" to teach three Machanos regarding Parah? He can learn it from Parim ha'Nisrafim, like we learn Mekalel [from Parim ha'Nisrafim] in Sanhedrin!

Answer: Perhaps R. Shimon learns also Mekalel from Par Yom Kipur, just like [he learns] Parah [from Par Yom Kipur].

Question: Also, according to us, we should learn that Mekalel is outside the Machaneh from Yom Kipur, which is Metamei Begadim outside of one Machaneh, and not learn three Machanos from Sereifas Parim!

Answer: It is more reasonable to learn from Sereifah. For both of these, the Hechsher (proper way to do the Mitzvah) is there - stoning the Mekalel and burning the bulls;

Tum'as Begadim outside one Machaneh is not its Hechsher.

Question: Why do we need in Zevachim 107b "ba'Machaneh" to teach that [one is liable for Shechutei Chutz] even outside of one Machaneh, so we will not say outside of three Machanos, like regarding Parim ha'Nisrafim?

Even without the verse, we should learn from "mi'Chutz la'Machaneh" of Tum'as Begadim, for both of them are similar. They are not Machshirim!

Answer: Had the Torah not written ba'Machaneh, we would have learned from Parah;

Implied question: We should not learn it, for this (Parah) is Machshir, and this (Shechutei Chutz) is not Machshir!

Answer: Even so, since both of them discuss Shechitah b'Chutz - regarding Parah it says "v'Hotzi Osah El mi'Chutz la'Machaneh v'Shachat Osah Lefanav" - we would learn them from each other.

We learn Parah from Parim ha'Nisrafim, from burning them, and not from their Tum'ah;

It is more similar to burning them, for both of these are Machshir. It is not like their Tum'ah at all.