Yevamot 51B

רבנן סברי יש זיקה, וקתני סיפא: וכן אתה אומר בשני יבמין ויבמה אחת. לימא תיהוי תיובתא דרבה בר רב הונא אמר רב. דאמר רבה בר רב הונא אמר רב: חליצה פסולה ⁠— צריכה לחזור על כל האחין.

it can be inferred that the Rabbis hold that the levirate bond is substantial, as it is assumed that they disagree with Rabban Gamliel in this regard as well. And the latter clause of that baraita teaches: And you would say the same with regard to two yevamin and one yevama such that if the two yevamin gave one yevama a bill of divorce, she is exempted by the ḥalitza of one of them. If so, let us say that it is a conclusive refutation of the statement that Rabba bar Rav Huna said that Rav said. For Rabba bar Rav Huna said that Rav said: In cases of invalid ḥalitza, the yevama is required to repeat the ḥalitza with all the brothers. If the ḥalitza was invalid for some reason, all the brothers must perform ḥalitza with the yevama, as her bond with them is not canceled by an invalid ḥalitza.

אמר לך רבה בר רב הונא: בין לרבן גמליאל בין לרבנן סברי אין זיקה, והכא בגט אחר גט ומאמר אחר מאמר קמיפלגי.

The Talmud responds: Rabba bar Rav Huna could have said to you: Both Rabban Gamliel and the Rabbis hold that the levirate bond is not substantial, whereas my statement is in accordance with the opinion that the levirate bond is substantial. And here the dispute does not concern the topic of the levirate bond at all, but rather it only involves the explicitly mentioned issue: They disagree with regard to the efficacy of a bill of divorce after a bill of divorce and levirate betrothal after levirate betrothal.

אמר מר: עשה מאמר בזו ומאמר בזו, רבן גמליאל אומר: נותן גט לראשונה וחולץ לה, ואסור בקרובותיה, ומותר בקרובות שניה. מכדי קסבר רבן גמליאל אין מאמר אחר מאמר, ראשונה נמי תתייבם? גזירה דלמא אתי לייבומי לשניה.

The Master said above in the baraita: If he performed levirate betrothal with this one and levirate betrothal with that one, Rabban Gamliel says: He gives a bill of divorce to the first one and performs ḥalitza with her and is forbidden to her relatives, but he is permitted to the relatives of the second one. The Talmud poses a question: Since Rabban Gamliel holds that levirate betrothal is not effective after levirate betrothal, and the second levirate betrothal is of no consequence, the first woman should also be permitted to enter into levirate marriage. Why must he perform ḥalitza with her? The Talmud answers: It is prohibited due to a rabbinic decree lest he perform levirate marriage with the second woman. The rabbis were concerned that in cases where the yavam performed levirate betrothal with both women, if he were permitted to consummate the levirate marriage with the first woman, he might do so with the second woman as well.