Shabbat 24B

ולית הילכתא ככל הני שמעתתא, אלא כי הא דאמר רבי יהושע בן לוי: יום הכפורים שחל להיות בשבת ⁠— המתפלל נעילה צריך להזכיר של שבת. יום הוא שנתחייב בארבע תפלות.

The Talmud concludes: And the halakha is not in accordance with any of these halakhot; rather, it is in accordance with that which R' Yehoshua ben Levi said: On Yom Kippur that falls on Shabbat, one who recites the day’s closing prayer [ne’ila] must mention Shabbat even in that prayer, although ne’ila is not recited every Shabbat. The reason for this is that on Yom Kippur, the day itself is obligated in 4 prayers, i.e., morning, additional, afternoon, and closing. When it occurs on Shabbat, one must mention Shabbat in each of the prayers. Apparently, on a day that has a unique character, that character is manifest in all sacred aspects of the day; those engendered by the day itself as well as those engendered by other factors.

קשיא הילכתא אהילכתא. אמרת הילכתא כרבי יהושע בן לוי, וקיימא לן הילכתא כרבא. דאמר רבא: יום טוב שחל להיות בשבת, שליח ציבור היורד לפני התיבה ערבית אינו צריך להזכיר של יום טוב, שאילמלא שבת אין שליח צבור יורד ערבית ביום טוב.

The Talmud challenges this: It is difficult, as there is a contradiction between one halakha and another halakha. On the one hand, you said that the halakha is in accordance with the opinion of R' Yehoshua ben Levi. And, on the other hand, we hold that the halakha is in accordance with the opinion of Rava, which contradicts the first halakha, as Rava said: On a Festival that occurs on Shabbat, the prayer leader who descends before the ark to recite the prayer abridged from the 7 blessings of the Shabbat evening Amida prayer need not mention the Festival, as, if it were not also Shabbat, the prayer leader would not descend before the ark to recite this prayer during the evening prayer on a Festival. The Talmud reverts to the previous assumption that an element that does not arise from the essential halakhot of the day is considered foreign to it and is not mentioned.