Yoma 88A

מפני שצריך לומר הבדלה בחונן הדעת! תנאי היא. דתניא: כל חייבי טבילות ⁠— טובלין כדרכן ביום הכפורים. נדה ויולדת ⁠— טובלות כדרכן בלילי יום הכפורים.

because he must recite havdala in the blessing: Who graciously grants knowledge, and there is nowhere to insert this prayer in the abridged Amida. This indicates that these tanna’im maintained that ne’ila does not exempt one from the evening prayer. The Talmud answers: It is a dispute between tanna’im, as it was taught in a baraita: Anyone who requires immersion immerses in his usual manner on Yom Kippur, as this act does not violate the prohibition against washing. A menstruating woman and a new mother, who immerse at night, immerse in their usual manner on the night of Yom Kippur.

בעל קרי ⁠— טובל והולך עד המנחה. רבי יוסי אומר: כל היום כולו.

The baraita continues: One who had a seminal emission during Yom Kippur before the afternoon prayer may immerse at any point in the day until the afternoon prayer, in order to be able to recite it. Ezra decreed that a man who has had a seminal emission must immerse in order to pray and study Torah. If the emission occurred after the afternoon prayer, he should not immerse then but should wait until darkness falls. Since the time for ne’ila is at night, this individual should wait and immerse after the fast has concluded, so as to avoid violation of the prohibition of washing on Yom Kippur, and then pray afterward. This indicates that ne’ila is a nighttime prayer, and therefore its recitation exempts one from the weekday evening prayer. R' Yosei says: He may immerse at any point in the day. According to his opinion, the ne’ila prayer is recited while it is still daytime, and therefore the individual must immerse in the daytime in order to be able to recite it. Consequently, R' Yosei holds that ne’ila does not exempt one from the evening prayer.