Nedarim, Chapter Six, Mishnah 6, which deals with the law of one who takes a vow not to eat meat.
"HaNoder min habasar - mutar barotev uvakipah" - one who vowed not to eat meat is permitted in these two things:
Rotev - the broth of the meat; he is permitted to eat or drink it.
Kipah - the residue that collects at the bottom of the pot after the meat is cooked. This too is permitted, and it is not considered meat.
"Rabbi Yehudah oser" - Rabbi Yehudah disagrees and holds that both the broth and the residue are included in the prohibition, since they carry the taste of meat, and they are therefore considered part of the meat itself.
Rabbi Yehudah's proof:
"V'amar Rabbi Yehudah: ma'aseh, v'asar alai Rabbi Tarfon beitzim shenisbashlu imo" - Rabbi Yehudah brings a proof for his position from an incident that happened to him personally: he had vowed not to eat meat, and Rabbi Tarfon ruled that because of his vow he was forbidden to eat eggs that had been cooked together with the meat. From here Rabbi Yehudah learned that the prohibition is not limited to the meat itself, but anything that carries the taste of meat is also forbidden to one who vowed not to eat meat.
The response of the Sages:
"Amru lo: v'chen hadavar, eimasai? Bizman sheyomar basar zeh alai" - the Sages disagreed with him and answered: it is indeed true that Rabbi Tarfon forbade the eggs, but in what case was this law stated? When the one who vowed said "this meat is forbidden to me," referring to a specific piece of meat.
The reason is that whenever a person vows against a specific item and that item becomes mixed into something else, if it imparts its taste to the mixture, the mixture is forbidden. From here comes the distinction the Sages draw:
One who vowed against meat in general: the broth and the residue are not included in the vow and are permitted to be eaten.
One who said "this meat is forbidden to me": anything that contains even the taste of that particular piece of meat is forbidden.
In summary: in this Mishnah the Sages and Rabbi Yehudah disagree about the law of one who vows not to eat meat. According to the Sages the broth and the residue are permitted, while according to Rabbi Yehudah they are forbidden because of the taste of meat in them. Rabbi Yehudah brought a proof from the incident in which Rabbi Tarfon forbade him eggs that had been cooked with meat, and the Sages rejected his proof and established that this law applies only when the vow was made against a specific piece of meat, in which case any mixture containing its taste is forbidden.