It looks like this Adam and Eve thing carried over into the New Testament era:
1 Timothy 2:9 "Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments, but rather by means of good works, as is proper for women making a claim to godliness. A woman must quietly receive instruction with entire submissiveness. But I do not allow a woman to teach or exercise authority over a man, but to remain quiet. For it was Adam who was first created, and then Eve. And it was not Adam who was deceived, but the woman being deceived, fell into transgression. But women will be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint. "
Did God really mean what He said? Yes, He did!
I know that many will take this to apply only to the roles in the church. Yet, it addresses a lot more than that even bringing in the matter of children.