We are beginning siman 11, where the Chayei Adam returns to discuss havdalah on a kos. The Chayei Adam writes that the same way there is a mitzvah to sanctify Shabbos when it comes in, so too, there is a mitzvah to sanctify it when it leaves. We have learned that the mitzvah of zachor es yom haShabbos lekadesho obligates us to say something about the uniqueness of Shabbos. The same way there is such a chiyuv at the beginning of Shabbos to point out how Shabbos is unique and special over the weekdays, so too there is such a chiyuv at the end of Shabbos. Thus, the chiyuv of havdalah parallels the chiyuv of kiddush.
The Chayei Adam writes that according to the Rambam, havdalah is a mitzvas asei mideoraysa, all part of the mitzvah of zachor es yom haShabbos lekadesho. However, other rishonim understand that havdalah is a mitzvah derabanan. One ramification of this machlokes would be if one is unsure whether they fulfilled their chiyuv of havdalah. If it is a chiyuv deoraysa, we pasken safeik deoraysa lechumra, and one would repeat havdalah, even though it is possible they are reciting brachos in vain. If it is a chiyuv derabanan, we pasken safeik derabanan lekulah, and one would not repeat. That being said, even according to the Rambam, it could be that since one can fulfill their chiyuv deoraysa of havdalah by saying the words baruch hamavdil bein kodesh lechol, or through atah chonantanu, even the Rambam would agree that a person should not repeat havdalah.
Similarly, the Mishnah Berurah points out that even according to the Rambam that havdalah is a chiyuv deoraysa, if a person recites atah chonantanu in shemoneh esrei, they have fulfilled their chiyuv deoraysa and performing havdalah on a kos becomes derabanan. This is in contrast to kiddush on Friday night, which is a machlokes. We learned that according to the Magen Avraham, one can fulfill their chiyuv deoraysa of kiddush through shemoneh esrei. However, the Mishnah Berurah raises the question that Chazal learn that there is a chiyuv to mention yetzias mitzrayim in kiddush, and yetzias mitzrayim is not mentioned in our shemoneh esrei. However, there is no chiyuv to mention yetzias mitzrayim in havdalah, so even the Mishnah Berurah would agree that one is yotzei their chiyuv deoraysa through atah chonantanu in shemoneh esrei.
Therefore, coming back to our case where a person is unsure if they made havdalah on a kos, if they know they davened shemoneh esrei and recited atah chonantanu, their question about havdalah on a kos becomes a safeik derabanan, so they would not repeat havdalah on a kos. If, for whatever reason, they are not going to daven maariv, or already davened maariv without reciting atah chonantanu, they now have a safeik deoraysa.
Either way, we conclude from this question that havdalah is part of the kavod of Shabbos, to the extent that the Rambam holds it is a chiyuv deoraysa.
In the next siman, the Chayei Adam will discuss whether women are chayav in havdalah. We know women are chayav in kiddush, because Chazal connect between the negative issurim of Shabbos (shamor) and the positive mitzvos of Shabbos (zachor), and learn that anyone chayav in the negative issurim is chayav in the positive mitzvos as well. Thus, if one learns the chiyuv havdalah is part the mitzvah deoraysa of zachor, women will be chayav in havdalah as well.
Summary
- According to the Rambam, havdalah is a mitzvah deoraysa. According to other rishonim, havdalah is a chiyuv derabanan. Either way, the Rambam will agree that if one recites atah chonantanu in shemoneh esrei, they have fulfilled their chiyuv deoraysa of havdalah and making havdalah on a kos becomes a chiyuv derabanan.