The 167th mitzvah is that we are commanded to refrain from doing melachah on the eighth1 day of Sukkos.
The source of this commandment is G‑d's statement,2 "The eighth day is a sacred holiday for you."
You must know that the command to refrain from melachah is identical for all of these six days,3 and not a single one of these days has a prohibited melachah unique to it that does not apply to the other. So too, we are allowed to prepare food on each one of them. Therefore, the same law of refraining from melachah applies to all Yomim-Tovim, the details of which are explained in Tractate Yom-Tov [Beitzah].
However, the law of refraining from melachah on Shabbos and Yom Kippur includes these types of melachah and many others as well, because preparation of food was not allowed on these two days. There are some categories of melachah4 which, although they do not involve food preparation, are still permitted on Yom-Tov and forbidden on Shabbos, as explained in Tractate Yom-Tov.5
