Gemara

100a (Rabah bar bar Chanah): If a piece of Nevelah fell into a pot, it forbids the contents only if the piece is big enough to give taste to the liquid, sediments, and pieces of meat in the pot.

(Rav): Once the Nevelah gives taste to another piece, that piece is itself like a Nevelah, and it forbids all the pieces, for they are Mino (the same type).

Question (Rav Safra): Rav's law is like R. Yehudah, who holds that Min b'Mino is never Batel. Even if the Nevelah didn't give Ta'am to another piece, it would forbid them all!

Answer #1 (Abaye): The case is, the Nevelah was removed from the pot before (some of) the other pieces were put in. They did not absorb from it at all.

(Beraisa - R. Yehudah): If a drop of milk fell on a piece of meat in a pot, and the milk gives Ta'am to the piece, it becomes like Nevelah, and forbids all the pieces, for they are Mino;

Chachamim say, they are forbidden only if it gives Ta'am to the sauce, sediments and pieces.

Rebbi: I agree with R. Yehudah when the pot was not stirred or covered. I agree with Chachamim when the pot was stirred or covered.

'Not stirred or covered' means at first, but it was stirred or covered later.

Question: The piece absorbs the Ta'am of the milk, and emits it. Even the piece should become permitted again!

Answer: R. Yehudah forbids Efshar Lesochto. (If food 'A' absorbed Isur and was forbidden, and then 'A' was cooked with enough Heter for Bitul, we do not say that the Isur exudes and 'A' is permitted.)

Rebbi agrees with Chachamim when the pot was stirred or covered, i.e. from the beginning. Chachamim permit even if it was stirred or covered only later. They permit Efshar Lesochto.

Avodah Zarah 73a (Ravin citing R. Yochanan): If Yayin Nesech fell into a pit of wine, and also water fell in, we ignore the Heter wine. If there is enough water to Mevatel the Yayin Nesech, it is permitted.

Version #1 (Rav Shmuel citing R. Yochanan): This is only if the water fell in before the Yayin Nesech. If the Yayin Nesech fell in first, it forbids the whole pit (and there is not enough water to Mevatel all the wine in the pit).

Version #2 (Rav Shmuel citing R. Yochanan): The Mishnah says that Yayin Nesech forbids b'Mashehu, i.e. if no water fell in. If also water fell in, we ignore the Heter wine, and if there is enough water to Mevatel the Yayin Nesech, it is permitted. (end of Version #2)

73b (R. Yochanan): If two cups of diluted wine, Chulin and Terumah, got mixed, we ignore the Chulin wine, and the water (if there is enough) is Mevatel the Terumah.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 9:8): If meat fell into milk or vice-versa and they became cooked, if it absorbed taste, it is forbidden. If he did not remove the piece before it emitted the milk inside, we estimate if there is 60, for the absorbed milk that became forbidden leaves and mixes with the rest of the milk.

Magid Mishneh: The Rambam applies CHaNaN (Chatichah Atzmah Na'asis Nevelah, i.e. a piece that was forbidden due to absorptions is considered like pure Isur) only to meat and milk. He did not mention it regarding other Isurim. In Hilchos Terumos (13:3) he said that Meduma (a mixture of Terumah and Chulin) forbids according to the calculation (of how much Terumah is contains). He did not distinguish it from other Isurim.

Rosh (7:38): Why did we need to say that the first piece absorbed enough Isur to give taste? R. Tam says that Mashehu would not suffice to forbid the other pieces. R. Efrayim applies CHaNaN only to meat and milk.

Ran (Sof 44b): In Version #1 in Avodah Zarah, we say CHaNaN even regarding a mixture of wet and wet. The Ramban says that Tana'im argue about this in a Mishnah (Temurah 12b). R. Yehoshua says that Mayim She'uvim (water that was in a Kli) disqualify (a Mikveh) only according to the calculation (of how much of the mixture is She'uvim). Chachamim consider the entire mixture to be like She'uvim. He says that they argue in every case, whether the Isur is wet or dry. Often, there is a contradiction between the Sugyos, and the Gemara does not ask.

Rebuttal (Ran): A Mikveh is different. If it began with three Lugim of She'uvim, no amount of water will be Mevatel them. They transform all water into She'uvim. That Mishnah does not discuss a mixture of She'uvim and Kosher water, rather, the number of Kelim from which the water fell. It says 'according to the calculation' for parallel structure with the clauses about Meduma. This is why it did not say 'a mixture of She'uvim and Kosher water forbids according to the calculation.' Rather, CHaNaN is mid'Oraisa for meat and milk, for each of them becomes Isur. For other Isurim, it is mid'Rabanan. We equate them to meat and milk, but only Derech Bishul, i.e. things cooked together, or cold that fell into hot. We do not say so for Meduma or a mixture of Isur and Heter sourdough, or Yayin that fell into Asur water. Why didn't the Rif rule that we say CHaNaN, to require a Shi'ur (for Bitul) corresponding to the entire piece? Some answer that CHaNaN is only according to R. Yehudah, who holds that Min b'Mino is not Batel, and we hold that it is Batel. The Yerushalmi refutes them. The Ramban explicitly says that even Chachamim say CHaNaN.

Poskim

Shulchan Aruch (YD 92:4): We say CHaNaN only regarding Basar v'Chalav, but not regarding other Isurim. E.g. if a k'Zayis of Nevelah was absorbed in a piece, and there are not 60 parts to be Mevatel it, and then it was cooked with others, we need 60 parts only corresponding to the k'Zayis, and then even the piece is permitted.

Beis Yosef (DH u'Pasak): R. Efrayim forbids Efshar Lesochto only regarding meat and milk. For other Isurim we need only 60 times the first k'Zayis. R. Tam forbids Efshar Lesochto regarding other Isurim, but only if the Isur gave taste. Abaye said that the Isur was removed (before more Heter fell in). Tosfos asked why Rav needed to say that the piece of Heter received taste from the Isur. Even if it did not, any amount of Mino forbids! R. Tam answered that even though any amount forbids the piece, it would not become like a Nevelah to forbid the others, since it was forbidden through any amount. R. Efrayim derived that even if it gave taste, we do not need 60 times the piece (for Bitul), rather, just 60 times the absorbed Isur. This is why Rav, who forbids Min b'Mino, says that when the Heter received taste from the Nevelah, it is as if the Isur is intact, and it forbids all the pieces b'Mashehu. If it did not give taste, it would not forbid them due to Mino, since we need to to be Mevatel only the Isur. Since the Isur did not give taste to the piece, it is as if it is not intact. CHaNaN applies only when milk fell onto meat, for each of them is permitted by itself, and together they are forbidden. The meat itself becomes Isur, and one is lashed for half a k'Zayis of the meat and half a k'Zayis of the milk. If a piece absorbed Nevelah and fell sick into liquid, we need only 60 times the amount of Isur absorbed.

Gra (16): This is like Avodah Zarah 73b. For other Isurim, we do not forbid Efshar Lesochto. This is from the Tur. In Siman 106, the Tur and Shulchan Aruch forbid even for other Isurim, i.e. when the Isur did not totally dissolve.

Taz (10): The Mechaber follows the Tur, who says that since Efshar Lesochto does not apply to other Isurim, the piece itself is permitted. In 106:1, he says oppositely. What he said there is correct.

Shach (11): Below (106:1), the Mechaber says that the piece itself remains forbidden. The Rema said that this is unlike he wrote here! I answer that above the Mechaber said that for meat and milk, even when the liquid is permitted, if the piece is Re'uyah Lehiskaved and it is not recognized, it is not Batel even in 1000. Here he teaches that for other Isurim, it is Batel is the majority, since it is not forbidden due to itself. (I.e. in 106, he discusses when the piece is recognized, so one must remove it - Machatzis ha'Shekel.)

Rema: Some apply CHaNaN to all Isurim. This is the custom. One should not deviate.

Beis Yosef (ibid.): The Ri said that we should be stringent, for there is no clear proof. Semag said that we should not be lenient like R. Efrayim, for all the early Chachamim disagree. The Mordechai (697) applies CHaNaN to other Isurim only to the piece itself, due to its importance. It is a recognized, separate Isur, and became forbidden by itself. How can Heter help to be Mevatel Isur absorbed in it?! We need enough to be Mevatel the entire piece if it is not Chatichah ha'Re'uyah Lehiskaved or Davar sheb'Minyan. However, regarding something wet, e.g. Terumah in Chulin, wine in water of idolatry, or gravy in gravy, there is no importance to the Isur. The second Heter joins with the first. CHaNaN does not apply at all. The Rashba, Ran and Ra'avad apply CHaNaN to Isur absorbed in a piece. The Isur does not leave the piece; it remains forbidden like a Nevelah. If the Isur and Heter are both wet, e.g. wine or water, even though it was initially forbidden, when more Heter falls in it totally mixes. Therefore, it forbids only according to the calculation. They rejected those who say oppositely, that CHaNaN is when both are wet and they totally mix.

Beis Yosef (ibid.): The Rashba says that R. Efrayim's opinion is primary. Efshar Lesochto is forbidden only for meat and milk, for it becomes total Isur. He admits that if a piece absorbed Isur and fell into a pot with 60 times the Isur, the piece is forbidden (if we recognize it), for the absorbed Isur does not mix with the Heter. The Rosh cited R. Tam and R. Efrayim, and did not decide between them. The Tur wrote that the Rosh holds like R. Efrayim, for in many places 'this is good according to R. Efrayim.' In some places, the Rosh says 'this is when enough did not fall in to give taste.' I.e. he teaches how R. Tam can explain. In a Teshuvah (20:2) he clearly holds like R. Efrayim. Perhaps the Tur learned from this Teshuvah.

Rema: This is only if the Isur clings to the Heter, or it is totally outside of the liquid and Isur fell on it. If part of the piece was in the liquid, and the Isur does not stick to it, we do not say CHaNaN, and the entire pot joins to be Mevatel the Isur. In any case one should be stringent to forbid the piece. This applies to other Isurim. For meat and milk, even if the Isur does not cling, and part is in the liquid, we say CHaNaN. Some do not apply CHaNaN if a wet Isur and Heter mixed, and later it was mixed with more Heter. We need 60 only based on the original Isur. One may rely on this for other Isurim to avoid a big loss, but not for meat and milk. If dry Isur and Heter mixed, we do not say CHaNaN for any Isur.

Taz (16): The Rema discusses a dry mixture without cooking. If it was cooked, the Isur would be Batel is the majority. If it was initially mixed with less Heter than itself, and later it was mixed with more Heter, a majority against the Isur suffices. If it was cooked, CHaNaN applies, and we need 60 times as much as the piece. The Tur says that R. Tam forbids Efshar Lesochto for other Isurim, and says CHaNaN, only if it was forbidden through taste, but not through Mashehu, even if the piece was forbidden due to Min b'Mino according to R. Yehudah. All the Poskim bring R. Tam. The Levush says that when Chametz or Yayin Nesech forbids b'Mashehu, it does not become Nevelah. If it falls into another pot, it is Batel is the majority. If one recognizes the Isur, he must dicard it. The Shulchan Aruch (OC 447:1) says that Chametz forbids b'Mashehu. This refers only to the first mixture. This is why the Tur said that CHaNaN does not apply to Chametz. The Bach said that he discusses Chametz after Pesach. This is wrong. However, if the first mixture was wet with wet, the second mixture does not help, for the Isur is never Batel. If a dry piece was forbidden through Mashehu, and it became mixed and we do not recognize it, the Shulchan Aruch (447:9) brings two opinions about whether it is Batel in the majority. It is proper to be stringent. The Levush himself says so there, unlike what he said here that it is Batel.

Shulchan Aruch (106:1): If a piece absorbed Isur and there were not 60 parts for Bitul, and it fell into a pot, it forbids only according to the calculation of absorbed Isur. If the pot has 60 times the amount of Isur, it is permitted, but the piece itself is forbidden.

Rema: This is unlike the Mechaber wrote in Siman 92:4, that the piece itself is permitted.