Gemara

Beraisa - R. Shimon: For any Davar she'Yesh Lo Matirim (there is a time, place or way in which the Isur is permitted), such as Tevel, Ma'aser Sheni, Hekdesh, and Chodosh, there is no Shi'ur (of Heter in which it is Batel);

For every Davar she'Ein Lo Matirim, such as Terumah, Terumas Ma'aser, Chalah, Orlah, and Kil'ai ha'Kerem, Chachamim fixed a Shi'ur (for Bitul).

Chachamim: Shemitah is never permitted, yet it is never Batel!

Mishnah: Any amount of Shemitah produce forbids b'Minah (if it became mixed with Heter of the same species)

R. Shimon: That is regarding (Ran - eating before) Bi'ur. Regarding eating (Ran - after Bi'ur), if they are not Nosen Ta'am, they are Batel (since Ein Lo Matirim).

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;

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

Answer (Rav Ashi): It is a Davar she'Yesh Lo Matirim. Such things are not Batel even in 1000.

3b - Beraisa: An egg laid on Shabbos or Yom Tov is Muktzeh. A Safek about it is forbidden. Even if it became mixed with 1000, they are all forbidden.

Question: According to Rabah, the egg is forbidden mid'Oraisa because of Hachanah, therefore a Safek is forbidden. Rav Yosef and R. Yitzchak forbid it mid'Rabanan. Why is a Safek forbidden?

Answer #1: The Beraisa forbids an (egg from a hen that is) Safek Tereifah.

Question: A mixture of 1000 is forbidden. Granted, if the Safek is whether or not it was laid on Shabbos or Yom Tov, this is Davar she'Yesh Lo Matirim. But if it is a Safek Tereifah, it should be Batel in the majority!

Answer: Eggs are sold by number. The Tana holds that such things are never Batel.

4a - Answer #2 (Rav Ashi): Davar she'Yesh Lo Matirim, even regarding an Isur mid'Rabanan, is not Batel even in 1000 (and likewise a Safek is forbidden).

4b - Rav Masnah: If wood fell from a date tree into an oven on Yom Tov, one may add to it a larger amount of Heter wood and light all of it.

Question: (When he moves the wood in the oven) he moves Isur!

Answer: The Muktzeh is Batel in the majority.

Question: One may not Mevatel an Isur l'Chatchilah!

Answer: One may not Mevatel an Isur mid'Oraisa l'Chatchilah, but one may Mevatel an Isur mid'Rabanan l'Chatchilah.

Question: Rav Ashi taught that Davar she'Yesh Lo Matirim is never Batel, even regarding an Isur mid'Rabanan!

Answer: That is when the Isur is intact. Here, the Isur is burned.

Rishonim

Rif and Rosh (Beitzah 2a and 1:2): If wood fell off a tree on Yom Tov, one may not burn it, for it is Nolad. It is Batel in a majority of Heter. Even though the Halachah follows Rav Ashi who says that Davar she'Yesh Lo Matirim is never Batel, that is when the Isur is intact. Here, the Isur is burned.

Rambam (Hilchos Yom Tov 1:19): One may not eat or move an egg laid on Yom Tov. Even if it became mixed with 1000 eggs, all are forbidden, because Davar she'Yesh Lo Matirim is never Batel.

Magid Mishnah: Since there is no Bitul, surely a Safek is forbidden, so the Rambam did not need to say this. Also, he forbids every Safek Muchan. A Beraisa (3b) forbids 'even if it became mixed with 1000'. Some say that this refers to a Safek. Others say that it refers to a Vadai Nolad egg, but if a Safek became mixed it is permitted.

Rebuttal (Lechem Mishneh): The Gemara knew that Davar she'Yesh Lo Matirim forbids a mixture of 1000, but it still asked why a Safek is forbidden! Rav Papa holds that Rav Yosef explains the Beraisa to discuss a Safek Tereifah, for he answers why it is not Batel! Even though Rav Ashi argues, it is not obvious that we forbid a Safek Davar she'Yesh Lo Matirim! Rather, the Rambam forbids Hachanah mid'Oraisa like Rabah, therefore it is obvious that we are stringent about a Safek.

Rambam (Hilchos Ma'achalos Asuros 15:10): If any amount of Chodosh (this year's grain, which is forbidden until the Omer is offered) was mixed with Yashan (last year's grain) it forbids, for it will all be permitted after the Omer. The same applies to every Davar she'Yesh Lo Matirim, even an Isur mid'Rabanan such as Muktzeh and Nolad on Yom Tov. Even several thousands of Heter are not Mevatel something that can be permitted, such as Hekdesh or Ma'aser (Sheni).

Radvaz: The Rambam mentions 'several thousands' to oppose the opinion that it is Batel in more than 1000.

Rosh (1:2): The Heter to Mevatel an Isur mid'Rabanan is only when the Isur gets burned. Otherwise, one may not Mevatel even an Isur mid'Rabanan.

Question: Granted, one does not benefit from the Isur until after it is burned. Why may one move it (amidst the mixture) before it is burned?

Answer (Mishbetzos Zahav YD 99:12): Perhaps the stringency of Yesh Lo Matirim applies to Hana'ah, but not to Tiltul. The Ran (below) supports this.

Ran (2b DH Aval): One may be Mevatel only a minor Isur mid'Rabanan such as moving Muktzeh, in a case when the Isur gets burned. Also, one may be Mevatel Terumah of Chutz la'Aretz, for it has no source mid'Oraisa.

Hagahos Ashri (DH Yisrael): We forbid Davar she'Yesh Lo Matirim even if the eggs were broken (to cook together), even though they lost their importance.

Poskim

Shulchan Aruch (OC 513:3): If an egg laid on Yom Tov was cooked b'Shogeg with other food, if there is 60 times its volume, all is permitted except for the egg. If one whitened food with it, something used for color or taste is not Batel.

Magen Avraham (7): The Shulchan Aruch permits if it did not affect the appearance, only the taste, even though it was to improve the food. This is like water and salt, which are Batel in a dough. Also the Rema (YD 102:1) forbids an egg used to stuff a chicken only because it affects the appearance.

Mishnah Berurah (9): The Gra (YD 102:6) and Shach (5,6) say that if it affects the appearance or taste, it is forbidden.

Shulchan Aruch (YD 102:1): Any Davar she'Yesh Lo Matirim, such as an egg born on Yom Tov, which is permitted the next day, is not Batel even in 1000.

Taz (1): Mid'Oraisa it is Batel in a majority. Chachamim were stringent to forbid eating it until it is permitted without Bitul.

Shulchan Aruch (ibid.): This is whether the egg is whole or broken. Even if it is a Safek whether or not it was born on Yom Tov, it forbids a mixture.

Gra (3): Here the Shulchan Aruch forbids Safek Davar she'Yesh Lo Matirim that became mixed; in Orach Chayim (513), he permits. (513:1 forbids a mixture containing Vadai Nolad. 513:2 forbids Safek Nolad itself.)

Taz (3): A normal Safek Isur mid'Rabanan is permitted, even if it is important.

Question: Rav Papa ate Chodosh (in Chutz la'Aretz) on the night of the (Safek 16th, Safek) 17th (Menachos 68b), even though Yesh Lo Matirim!

Answer (Bach DH Kol): Mordechai ha'Aruch says that the calendar was fixed, so we are lenient. R. Yom Tov calls this Ein Lo Matirim, because Chodosh becomes forbidden again (next year). However, we said (4b) 'according to Rav Ashi, even an Isur mid'Rabanan she'Yesh Lo Matirim is not Batel. How can we answer?' R. Shmuel infers from this that the Halachah is unlike him.

Bach (DH u'Mah she'Chasav v'Afilu): When needed, one may rely on those who permit a Safek Davar she'Yesh Lo Matirim that became mixed with a majority of Heter. All permit if one of this mixture became mixed with Heter.

Rebuttal (Shach 2): Some forbid the second mixture, i.e. Siman 110:8.

Bach (102 Sof DH u'Mah she'Chosav Aval): It would seem that we are lenient about a mere absorption without any real substance. However, the Rashba disagrees. He applies Yesh Lo Matirim to a Keli that absorbed Isur, because the Heter does not come by itself. The Ran and Terumas ha'Deshen agree. Also the Rambam (Nedarim 5:12) forbids a barrel due to one drop of wine, even though it is not intact. One may not rely on Isur v'Heter, who permits.