Gittin 81A

זכות הראויה לשני.

The Talmud answers: It is not referring to the right of a second man that she already married, but rather to the right that is due to a suitor who wishes to become her second husband, meaning that the first husband cannot eliminate the right of a second man who wishes to marry her.

מתני׳ כתב לגרש את אשתו, ונמלך; בית שמאי אומרים: פסלה מן הכהונה. ובית הלל אומרים: אף על פי שנתנו לה על תנאי, ולא נעשה התנאי ⁠– לא פסלה מן הכהונה.

Mishnah: If one wrote a bill of divorce to divorce his wife, and reconsidered and did not give it to her, Beit Shammai say: Although merely writing the bill of divorce does not dissolve the marriage, by doing so he disqualified her from marrying into the priesthood. And Beit Hillel say: Even if he gave the bill of divorce to her conditionally and the condition was not fulfilled, and therefore the bill of divorce did not take effect, he did not disqualify her from marrying into the priesthood. A woman is disqualified from marrying into the priesthood only if the divorce takes effect.

גמ׳ שלח ליה רב יוסף בריה דרב מנשה מדויל, לשמואל: ילמדנו רבינו, יצא עליו קול ⁠– ״איש פלוני כהן כתב גט לאשתו, ויושבת תחתיו ומשמשתו״, מהו?

Talmud: Rav Yosef, son of Rav Menashe from Devil, sent a query to Shmuel: Our teacher, instruct us. In the case of a priest about whom the following rumor circulated: So-and-so the priest wrote a bill of divorce to his wife, but she is still residing under his roof and attending to him; what is the halakha? Need one lend credence to this rumor?

שלח ליה: תצא, והדבר צריך בדיקה. מאי היא? אילימא דאי מבטלינן קלא או לא מבטלינן; והא נהרדעא אתריה דשמואל היא, ובנהרדעא לא מבטלי קלא! אלא דאי קרו לנתינה ״כתיבה״.

Shmuel sent the following response to him: She must leave her husband; but the matter requires investigation before he is forced to divorce her. The Talmud asks: What is the investigation that is required? If we say that the investigation is whether we can abolish the rumor that circulated, or we cannot abolish it; that cannot be the question: But isn’t Neharde’a the place where Shmuel is the halakhic authority and the rulings there are in accordance with his opinion, and in Neharde’a they do not abolish a rumor? Rather, the required investigation is to determine whether people in that place refer to giving a bill of divorce as writing. If that is the case, the rumor would be that he gave her a bill of divorce.