Gittin 4A

וחתמו ונתנו לה ⁠– כשר! וכי תימא אנן מדאורייתא קא מתנינן לה, אי הכי, ״אומר היה רבי מאיר דבר תורה״ מיבעי ליה!

and he signed it and gave it to his wife, it is a valid bill of divorce? And if you would say that we learned that this statement of Rav Naḥman applies by Torah law, whereas by rabbinic law R' Meir concedes that a bill of divorce must be written for her sake, if so, Rav Naḥman should have said: R' Meir would say that by Torah law if a husband found a document in the garbage he may use it.

אלא לעולם רבי אלעזר היא, וכי לא בעי רבי אלעזר חתימה ⁠– היכא דליכא עדים כלל; היכא דאיכא עדים ⁠– בעי. דאמר רבי אבא: מודה רבי אלעזר במזוייף מתוכו, שהוא פסול.

Rather, the Talmud retracts the previous answer and states: Actually, the Mishnah is in accordance with the opinion of R' Elazar, and when does R' Elazar not require that the signing must be for her sake? Where there are no witnesses at all on the bill of divorce. However, where there are witnesses, he does require that all their signatures must be for her sake. The proof for this is that R' Abba says: R' Elazar concedes with regard to a document whose falsification is inherent in it, i.e., a document that is signed by disqualified witnesses, that it is invalid. This shows that although R' Elazar maintains that a lack of signatures does not invalidate a bill of divorce, all signatures included in the bill of divorce must be valid; otherwise the document is rendered invalid.

רב אשי אמר: הא מני? רבי יהודה היא, דתנן: רבי יהודה פוסל, עד שתהא כתיבתו וחתימתו בתלוש.

Rav Ashi said a different explanation: In accordance with whose opinion is this Mishnah? It is in accordance with a third opinion, that of R' Yehuda. As we learned in a Mishnah (21b): R' Yehuda invalidates a bill of divorce unless its writing and signing are performed on an item that is detached from the ground. According to this opinion, both the writing and the signing must be done for her sake.