Gemara

Mishnah: If someone forbade a food and it became mixed with other food, if the forbidden food can be tasted, the mixture is forbidden.

Beitzah 37a - Mishnah: If Leah borrowed from Rachel spices, water or salt to make a dough, the dough may not be taken outside their common Techum;

R. Yehudah says, if she borrowed water we are not concerned for Rachel's Techum, for water is insignificant.

38a - Question: Why isn't the water and salt Batel to the dough?

Answer #1 (R. Aba): Rachel's property cannot be Batel in Leah's.

Objection (R. Oshaya): Min b'Eino Mino is Batel. And even Min b'Mino is Batel according to Chachamim of R. Yehudah!

Answer #2 (Abaye): Chachamim decree that water and salt are not Batel lest the women make a joint dough (and each will permit it in her entire Techum).

Answer #3 (Rava): Spices are added to give taste, so they are not Batel. (Also water is not Batel, for it is essential to the dough.)

Answer #4 (Rav Ashi): It is a Davar she'Yesh Lo Matirim (there is a time, place or way in which the Isur is permitted). Such things are not Batel even in 1000.

Rishonim

The Rif brings our Mishnah (a food forbidden by a Neder forbids a mixture b'Nosen Ta'am).

Ramban: This is b'Eino Mino, like R. Yehudah's case of eggs cooked with meat. B'Mino any amount forbids, for the Gemara (59a) says that Nedarim are Davar she'Yesh Lo Matirim. We learned that Davar she'Yesh Lo Matirim is not Batel. Our Mishnah teaches that this is only Min b'Mino. Min b'Eino Mino it forbids b'Nosen Ta'am.

Question: Any amount should forbid, for Nedarim are Yesh Lo Matirim!

Answer (Rosh 6:3): That is only Min b'Mino. Our Mishnah discusses Min b'Eino Mino. Regarding Min b'Eino Mino, the Yerushalmi says that Isurim forbid b'Nosen Ta'am, whether or not Yesh Lo Matirim.

Rambam (Hilchos Ma'achalos Asuros 15:9): Chametz b'Pesach is Asur mid'Oraisa. It is unlike other Isurim, because a mixture of Chametz is permitted after Pesach. Therefore, any amount of Chametz forbids (food it is mixed with), whether Min b'Mino or Min b'Eino Mino.

Kesef Mishneh: R. Yochanan and Reish Lakish (Avodah Zarah 73b) say that all Isurim in the Torah forbid b'Nosen Ta'am, whether Min b'Mino or b'Eino Mino, except for Tevel and Yayin Nesech. The Rambam explains that they could agree that Chametz forbids b'Mashehu, for they did not discuss Davar she'Yesh Lo Matirim.

Rambam (ibid. 12): It seems to me that even if Davar she'Yesh Lo Matirim was mixed with b'Eino Mino and did not give taste it is permitted. Davar she'Yesh Lo Matirim should not be more stringent than Tevel, which can be permitted (by tithing it), and nevertheless it is Batel Lo b'Mino if it did not give taste. Chametz b'Pesach is more stringent because the Torah forbids "Kol Machmetzes".

Question (Ra'avad): (Why does the Rambam say 'it seems to me'?) A Mishnah explicitly teaches about this!

Answer #1 (Radvaz): The Ra'avad alludes to a Mishnah in Shevi'is (7:7). It gives a general rule that anything that is Nosen Ta'am obligates Bi'ur; Min b'Mino (obligates Bi'ur) b'Mashehu. This rule applies to all Isurim. The Rambam does not rely on this Mishnah because the Halachah does not follow the Seifa; we hold that Min b'Mino is Batel in 60. Rather, he relies on his reasoning that Davar she'Yesh Lo Matirim should not be more stringent than Tevel. The Ra'avad holds that even though the Halachah does not follow the Seifa (it is like R. Yehudah), the Halachah follows the Reisha (there is no source that anyone argues).

Answer #2 (Kesef Mishneh): The Rif (Chulin 32b) says that if bread was baked with meat, all forbid eating it with milk. (Even though it is Min b'Eino Mino,) it is not Batel even in 1000 because it has Matirim, i.e. it can be eaten without milk). Rav Ashi (Beitzah 39a) says that water and salt cannot be Batel in a dough because Yesh Lo Matirim; this supports the Rif. The Ra'avad refers to this Mishnah of the dough, like Rav Ashi explains it.

Rebuttal (Rashash, in Likutim in Frankel Rambam): (If the Ra'avad meant that a Mishnah explicitly refutes the Rambam he would have explicitly said so!) This Mishnah shows that Yesh Lo Matirim is not Batel even b'Eino Mino!

(Kesef Mishneh (continuation): The Rambam holds that this is not a proof, for water and salt are considered the same Min as the dough. Alternatively, the Ra'avad learns from the Mishnah that says that a food forbidden by a Neder forbids b'Nosen Ta'am. The Yerushalmi (Nedarim 21b) considers this Yesh Lo Matirim, and establishes the Mishnah to discuss Min b'Eino Mino.

Poskim

Shulchan Aruch (OC 513:3): If a Nolad egg (laid on Yom Tov) was cooked b'Shogeg with a Tavshil (cooked food), if there is 60 times the egg's volume, everything except for the egg is permitted. If it whitened the Tavshil, anything done for color and taste is not Batel.

Beis Yosef (DH v'Avi): If a Safek Nolad egg was used to whiten a Tavshil or stuff a chicken, Avi ha'Ezri forbids it. R. Tam says that a Davar she'Yesh Lo Matirim is not Batel when it is intact, but its taste is Batel in 60. The Tur says that R. Tam would permit here, for he did not intend for Bitul. It seems that even R. Tam forbids, for it is added for color or taste. Also the Rosh and Sha'arei Dura forbid. Seemingly, the Rosh argues with the Rambam (above, 15:12). However, perhaps the Rosh holds like Tosfos (30a DH mi'Shum) that anything essential for a Tavshil is considered Mino.

Beis Yosef (DH Kosav ha'Kol): The Kol Bo permits a Tavshil in which a Nolad egg was cooked, because (whole) eggs do not give taste. In any case R. Tam permits, since the taste in Batel in 60.

Magen Avraham (6): 'Except for the egg' connotes that the egg is whole. It is permitted only because it is Min b'Eino Mino, but if it was cooked with eggs they would be forbidden. The Rema (YD 102:4) argues. He says that the taste of Davar she'Yesh Lo Matirim is Batel (even Min b'Mino).

Mishnah Berurah (8) and Sha'ar ha'Tziyon (14): Many argue with the Rema. If there is a great need, one may rely on the Rema, for Simchas Yom Tov.

Question (Taz 3): The Kol Bo and Shulchan Aruch (YD 86:5) permit even if there is not 60 times as much! Why does the Shulchan Aruch here require 60 times? If he discusses an egg with a hole in the shell (it gives taste), he should have specified. Also, the Shulchan Aruch discusses the Kol Bo's case!

Answer (Magen Avraham 7 and Gra DH Im): Here we require 60 because the shell was removed.

Shulchan Aruch (YD 102:1): Any Davar she'Yesh Lo Matirim is not Batel, even if it became mixed with 1000. If it became mixed with Eino Mino it is Batel in 60.

Source (Taz 5): The Ran (Nedarim 52a) explains that R. Yehudah says that Min b'Mino is never Batel because the minority strengthens the majority. Chachamim hold that Min b'Mino is Batel in Isurim, because Isur and Heter are like different Minim. Davar she'Yesh Lo Matirim is like the same Min as the Heter, for it will be permitted. However, this applies only Min b'Mino.

Shach (4): Regarding a Briyah or a Chatichah ha'Re'uyah Lehiskaved we do not distinguish whether it was mixed with Mino or Eino Mino. Here is different, for the importance of the Isur does not prevent Bitul. Rather, Chachamim do not allow Bitul for something that will be permitted without Bitul. Regarding Min b'Eino Mino, Bitul permits the majority, but we do not say that the Isur itself was permitted.

Rema: However, if it was used to whiten a food, or to fix a pot (of food), e.g. to stuff a chicken, it is not Batel.

Taz (6): Anything necessary for the food is considered Mino (and is never Batel). This is why mid'Oraisa Min b'Eino Mino is not Batel in a majority when it is Nosen Ta'am.