So... saying the president must be at least 35 years old isn’t a clear prohibition against ineligibility? Qualification: a condition or standard that must be complied with (as for the attainment of a privilege) a qualification for membership
Prohibition: the act of prohibiting by authority
Prohibition... qualification. Both very simple constitutional requirements. That is, until a democrat pushes against one of those, then all kinds of people go wobbly, including freepers.