Bava Batra 127B

זה לזה.

each to the other.

מה נפשך? אי כרבנן סבירא ליה, לישלח להו כרבנן; אי כרבי יהודה סבירא ליה, לישלח להו כרבי יהודה!

The Talmud questions this ruling: Whichever way you look at it, Shmuel’s opinion is difficult. If he holds in accordance with the opinion of the Rabbis with regard to this issue, he should have sent them a response in accordance with the opinion of the Rabbis, and if he holds in accordance with the opinion of R' Yehuda, he should have sent them a response in accordance with the opinion of R' Yehuda. Shmuel’s response is not in accordance with either tannaitic opinion.

מספקא ליה אי כרבי יהודה אי כרבנן.

The Talmud answers: He is uncertain whether the halakha is in accordance with the opinion of R' Yehuda or in accordance with the opinion of the Rabbis. Therefore he sent them a response that incorporates both opinions.

מאי היא? דתניא: ״יכיר״, יכירנו לאחרים.

The Talmud explains: What is the dispute between R' Yehuda and the Rabbis? As it is taught in a baraita: Expounding the verse: “He should acknowledge the firstborn” (Deuteronomy 21:17), the rabbis said: He should acknowledge him to others. In other words, a father is deemed credible to tell others that this is his firstborn.

מכאן אמר רבי יהודה: נאמן אדם לומר: ״זה בני בכור״. וכשם שנאמן אדם לומר ״זה בני בכור״, כך נאמן אדם לומר ״זה בן גרושה״ ו״זה בן חלוצה״. וחכמים אומרים: אינו נאמן.

From here, R' Yehuda says that a man is deemed credible to say: This is my firstborn son, even if he has sons presumed to be older. And just as a man is deemed credible to say: This is my firstborn son, so too, a man who is a priest is deemed credible to say about his son: This is a son of a divorced woman, or: This is a son of a yevama who has performed ḥalitza [ḥalutza], in which cases he is disqualified from the priesthood due to his flawed lineage [ḥalal]. And the Rabbis say: He is not deemed credible.