Berakhot 21B

או צבור וצבור, אבל יחיד לגבי צבור כמאן דלא צלי דמי, קמשמע לן. ואי אשמעינן הכא, משום דלא אתחיל בה, אבל התם דאתחיל בה ⁠— אימא לא. צריכא.

or a case where he prayed as part of a congregation and began to repeat it as part of a congregation; however, in a case where he initially prayed by himself and subsequently joined the congregation at the venue where it was praying, we might have said that an individual vis-à-vis the congregation is considered as one who has not prayed. Therefore, he taught us that in this case, too, one may not repeat the prayer. And, on the other hand, if he had taught us here only with regard to one who entered a synagogue, we would have thought that the reason he may not pray again is because he did not yet begin to recite the prayer, but there, in the case where he already began to recite the prayer, say that this is not the case and he may continue to repeat the prayer. Therefore, both statements are necessary.

אמר רב הונא: הנכנס לבית הכנסת ומצא צבור שמתפללין, אם יכול להתחיל ולגמור עד שלא יגיע שליח צבור ל״מודים״⁠ — יתפלל. ואם לאו ⁠— אל יתפלל. רבי יהושע בן לוי אמר: אם יכול להתחיל ולגמור עד שלא יגיע שליח צבור ל״קדושה״⁠ — יתפלל, ואם לאו ⁠— אל יתפלל.

Rav Huna said: One who did not yet pray and enters a synagogue and found that the congregation is in the midst of reciting the Amida prayer, if he is able to begin and complete his own prayer before the prayer leader reaches the blessing of thanksgiving [modim], he should begin to pray, and, if not, he should not begin to pray. R' Yehoshua ben Levi said: If he is able to begin and complete his prayer before the prayer leader reaches sanctification [kedusha], then he should begin to pray. If not, then he should not begin to pray.