shabbas 111a -- female sirus

The Gemara states that if we hold that women have a mitzva of פריה ורביה, then this would mean that sirus is assur for them. What is the connection -- animals don't have such a mitzva and it is still assur?
The Minchas Chinuch explains that really the issur of sirus is not dependent on פריה ורביה, based on what we stated above -- that animals are included. Rather, the point of the gemara is that even though women are NOT included in the issur of sirus based on גזירת הכתוב (the source is from the toras kohanim), the gemara suggests a second reason that is independent that would forbid them to drink the כוס של עיקרין, which is פריה ורביה.
Another interesting peshat point in the Minchas Chinuch is that based on the reading of the peshat of our gemara he takes issue with the pesak of the Rambam who paskens that there is a different level of issur if you do direct or indirect sirus. For a man, direct sirus is chayav malkus, while כוס של עיקרין is only assur and for women it goes down one level, where direct is assur and כוס של עיקרין is mutar. He says that the answer of direct vs indirect in the sugya was rejected, thus the pesak should be that one is chayav malkus for a male either way and for a female it should be mutar either way, including a woman due to not being commanded in פריה ורביה.