Gemara

99b (Mishnah - R. Yehudah): One measure of Tamei fish brine forbids a mixture of 192 measures.

Question: R. Yehudah holds that Min b'Mino is never Batel!

Answer: Brine is an exception. It is a mere Pirsha (secretion, or waste).

120a (Reish Lakish): "A soul (that will eat Chelev)" includes one who drinks (melted Chelev). "A soul (that will eat Chametz)" includes one who drinks (melted Chametz). "A soul (that will eat the Neveilah of a Tahor bird)" includes one who drinks.

Bechoros 6b - Question (Rav Acha): Chachamim learn (to forbid camel milk) from "Gamal... Gamal." R. Shimon learns from "Es ha'Gamal." If not, we would permit;

Why don't learn from Sheratzim (that what comes from something forbidden is forbidden)?

(Beraisa): "Ha'Teme'im" forbids their brine, soup (the water in which they were cooked), and Kipah (spices and shredded meat that accumulate at the bottom of the pot).

Answer: Normally, anything that comes from a living being is forbidden. Since the Torah permits milk, one might have thought that it permits even milk of Teme'im. Therefore, the verse is needed.

Question: What is the source that Tahor milk is permitted?

Answer #1: We learn from "v'Dei Chalev Izim l'Lachmecha l'Lechem Beisecha v'Chayim l'Na'arosecha" (that one may subsist on milk)!

Rejection: Perhaps the verse teaches that one will sell the milk (to Nochrim)!

Answer #2: "(David brought) v'Es Aseres Charitzei he'Chalav" (to the leader of 1000 men in the war. Surely, it may be eaten!)

Question: Perhaps he brought it to him to sell!

Answer: In war, one does not sell food to the enemy!

Answer #3: "Eretz Zavas Chalav u'Devash" - Eretz Yisrael would not be praised for something forbidden to eat!

Answer #4: "U'Lechu Shivru b'Lo Chesef uv'Lo Mechir Yayin v'Chalav."

Bechoros 23b (Beraisa): "Lo Sochlu Chol Neveilah la'Ger (...Titnenah va'Achalah)" - it is called (and forbidden like) Neveilah only if a Ger would eat it.

Avodah Zarah 40a (Rav Huna): The head and spine (of fish) must be recognizable.

(Rav Nachman): The head or spine must be recognizable.

(Rav Yehudah): They argue only about the brine. Both forbid the fish itself unless both the head and spine are recognizable.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 5:3): One who eats a k'Zayis of Ever Min ha'Chai is lashed. Even if he ate a whole limb, he is lashed only if it is a k'Zayis. If one cut off a k'Zayis from a limb the way it lives, with bones, sinews and meat, and ate it, he is liable even if there was only a small amount of meat.

Rebuttal (Ra'avad): He is exempt if there is not a k'Zayis of meat.

Pri Chodosh (62:3): The Rambam is correct. A support is the Gemara which says that milk is like Ever Min ha'Chai.

Pleisi (62:1): This is no support. All agree that milk would be forbidden (if not for a Chidush), just like Chetzi Shi'ur (of Ever Min ha'Chai). The Ra'avad holds that the Hava Amina was to forbid milk, but without lashes, like Chetzi Shi'ur. According to the opinion that Ta'am k'Ikar is mid'Oraisa, if a full limb gives taste to food in a pot, one is lashed for eating it, like for the limb itself. Likewise, the Hava Amina was to forbid milk due to "ha'Teme'im", which forbids brine and gravy (of Tamei species).

Ramban (Hilchos Bechoros 4a DH Beitzas): The Torah permitted eggs of Tahor birds, even though they come from a living being. Chizkiyah taught that "Bas ha'Ya'anah" forbids Tamei eggs. We infer that Tahor eggs are permitted. Bahag says so. If so, why don't we say the same about milk? Since the Torah needed to teach that milk of a camel is forbidden, this shows that milk of a Tahor animal is permitted! I say that it is because the Torah did not explicitly forbid milk of Tamei animals. The Torah listed the four animals with one Siman of Taharah (in Shemini), and repeated them (in Re'eh) for the sake of the Shesu'ah. There was no need to expound the repetition, but if we can find a Drashah, we expound it. Had the Torah not permitted milk of Tahor animals, we would have forbidden it, and not expounded Gamal-Gamal.

Rosh (Avodah Zarah 2:42): We are more than lenient about the brine than about the fish itself. This suggests that the brine (of Tamei fish) is forbidden only mid'Rabanan. Also Chulin 99b suggests like this. It seems that it is Batel Min b'Mino, even according to R. Yehudah, because it is a mere Pirsha. However, Bechoros 6b connotes that it is mid'Oraisa. We asked why we need a verse to forbid milk of a Tamei animal. We should learn from brine. This implies that it is a proper Drashah. In Chulin 120a, the Gemara explained why we need verses for brine of Tamei animals, and melted Chelev and Chametz. This shows that it is a proper Drashah. However, brine of Tamei fish is forbidden only mid'Rabanan. Toras Kohanim expounds to forbid it from "Sheketz". That Drashah is a mere Asmachta.

Tosfos (Chulin 99b DH She'ani): Brine of Tamei fish is forbidden only mid'Rabanan. The Torah forbade liquids only from Sheratzim and Tamei animals. Toras Kohanim expounds "Sheketz" to forbid brine of Tamei fish. This is a mere Asmachta. However, it is difficult how Rava brought a proof from "ha'Temei'im" to forbid brine of a Tereifah animal.

She'alas Ya'avetz (2:188): This is entire Tosfos is difficult. What forces us to learn all of the Sugyos unlike the simple reading, and say that a proper Drashah is a mere Asmachta without a real need? Sheketz is repeated in the verse for this Drashah! Why is ha'Temei'im a truer Drashah? Even though the Gemara said that brine is a mere Pirsha, why is fish brine different than brine of Sheratzim? Also it is a mere Pirsha, and it is less (worthy to forbid) than fish brine! Also the Rosh says that brine is forbidden only mid'Rabanan. Tosfos in Avodah Zarah explained otherwise. R. Tam suggested that brine of the fish itself is mid'Oraisa, but what comes out only through pickling in water and salt is only mid'Rabanan. This is what the Gemara calls a mere Pirsha.

Tosfos (Avodah Zarah 40a DH Machlokes): We expound (Chulin 112b) that brine (of Tamei fish) is forbidden, i.e. mid'Oraisa! Indeed, it is forbidden mid'Oraisa. However, it is Batel in a majority (Min b'Mino). The fish itself is not Batel, for it is a Briyah (full creation).

Poskim

Shulchan Aruch (YD 81:5): Milk and whey of Tahor animals are permitted.

Shach (12): The Gemara learned from a verse that milk is permitted. It is not like Ever Min ha'Chai or Basar Min ha'Chai. After the Torah permitted milk, this shows that "Lo Sochal ha'Nefesh Im ha'Basar", which forbids Ever Min ha'Chai, refers only to the meat of the animal. If so, all the more so whey is permitted.

Question (Teshuvas Chasam Sofer YD 70): There was no Hava Amina to say that milk is Ever Min ha'Chai or Basar Min ha'Chai. Rather, the Hava Amina is that it was like brine of Isur. In the entire Torah, liquids that exude from Isur are like the Isur (Chulin 120a). In Chulin, Tosfos says that for fish it is only mid'Rabanan. In Avodah Zarah, he holds that even fish is mid'Oraisa. This is primary. It is clear that Bechoros 6b is based on "ha'Teme'im". Milk is brine of Ever Min ha'Chai. One might have thought that since the Torah permitted it, it permits also milk (i.e. brine) of Temei'im. Gamal Gamal teaches that this is not so.

Afarkasta d'Anya (2 YD 127): Semag connotes that the Hava Amina is due to Ever Min ha'Chai. This requires investigation.

Teshuvas Chasam Sofer (YD 19): We must be concerned that for Nochrim, eggs are Ever Min ha'Chai. One may not invite Nochrim to eat food kneaded or cooked with eggs. Do not say that Ta'am k'Ikar (if an Isur can be tasted in a mixture, the mixture is forbidden like the Isur) does not apply to Nochrim. Rashi says that without a verse, we would say that the minority is Batel to the majority. For Nochrim, there is no source to follow the majority! Even one part in 1000 is not Batel. If eggs were once cooked in a pot, food cooked in it is forbidden to Nochrim, even if it is Nosen Ta'am li'Fgam (the absorbed taste in the pot is detrimental). This is not only according to the Poskim who forbid Nosen Ta'am li'Fgam whenever there is no Bitul. Even those who disagree learn to permit Nosen Ta'am li'Fgam from the Heter of a Neveilah not proper for a Ger to eat. This Heter is only for Yisrael. All of this requires investigation.

Va'Ya'an Yosef (YD 6 DH uv'Zeh): The Ra'avad (Ma'achalos Asuros 5:12) says that one is liable for Ever Min ha'Chai only for a full limb. The Pri Chodosh (62:3) supports the Rambam from milk, which is a Chidush, for it should have been Ever Min ha'Chai. I.e. surely milk is not Basar Min ha'Chai. Rather, the Hava Amina is that it is Ever Min ha'Chai, for it is part of the udder. The Pleisi says that the Ra'avad holds that the Hava Amina was to forbid due to Chetzi Shi'ur or Ta'am k'Ikar. I say that the same applies to eggs. Once they are finished, they are not meat. One may eat them with milk. The only Hava Amina to forbid them is due to Ever Min ha'Chai. However, they are not full limbs, for they were attached to the Eshkol (branches in the bird that hold eggs) and separated. The Torah needed to permit them to Yisrael, for we would have forbidden due to Chetzi Shi'ur or Ta'am k'Ikar. Tosfos (Chulin 33a DH Echad) holds that the Torah forbids only a k'Zayis to Nochrim, for this is Achilah. This is unlike the Rambam, who holds that Shi'urim are only for Yisrael. The Chasam Sofer holds that Ta'am k'Ikar is forbidden to Nochrim. Other Acharonim were unsure. Melei ha'Ro'im says that it depends on whether Chetzi Shi'ur is forbidden to them. If so, according to the Ra'avad, according to Tosfos, we do not need a verse to permit eggs or milk to Nochrim.