Berakhot 27A

היינו רבנן!

is identical to the opinion of the Rabbis, as the end of the period that begins with the midpoint of the afternoon is sunset.

אלא מאי, עד ולא עד בכלל? אימא סיפא: ושל מוספין כל היום. רבי יהודה אומר: עד שבע שעות. ותניא: היו לפניו שתי תפלות, אחת של מוסף ואחת של מנחה ⁠— מתפלל של מנחה ואחר כך של מוסף, שזו תדירה, וזו אינה תדירה. רבי יהודה אומר: מתפלל של מוסף ואחר כך של מנחה, שזו עוברת, וזו אינה עוברת.

The Talmud immediately rejects this proof: Rather, what is the alternative? That until means until and not including? It remains problematic. Say the latter clause of the Mishnah: The additional prayer may be recited all day. R' Yehuda says: It may be recited until the 7 hours. And it was taught in a baraita: If the obligation to recite two prayers was before him, one the additional prayer and one the afternoon prayer, he prays the afternoon prayer first and the additional prayer after that, because this, the afternoon prayer, is recited on a frequent basis, and that, the additional prayer, is recited on a relatively infrequent basis as it is only recited on Shabbat, Rosh Chodesh, and Festivals. The principle states: When a frequent practice and an infrequent practice clash, the frequent practice takes precedence over the infrequent practice. R' Yehuda says: He recites the additional prayer first and the afternoon prayer after that, because the time to recite this, the additional prayer, will soon elapse, and this, the time to recite the afternoon prayer, will not soon elapse, as one may recite it until the midpoint of the afternoon.

אי אמרת בשלמא ״עד ועד בכלל״, היינו דמשכחת להו שתי תפלות בהדי הדדי. אלא אי אמרת ״עד ולא עד בכלל״, היכי משכחת להו שתי תפלות בהדי הדדי? כיון דאתיא לה של מנחה, אזלא לה של מוספין!

The relevant point is: Granted, if you say that until means until and including, that is how you can find a situation where the times to recite two prayers, the afternoon prayer and the additional prayer, overlap. But if you say that until means until and not including, and that until 7 hours means until the beginning of the 7th hour, noon, then how can you find a situation where the times to recite two prayers overlap? Once the time to recite the afternoon prayer, a half hour past noon, has arrived, the time to recite the additional prayer is already gone?