quantum chemistry - How to derive Pauli Exclusion Principle without assuming anti-symmetry?

So, it appears that the statement of the Pauli Exclusion Principle is equivalent to the statement that fermions are anti-symmetric. That is, if you assume that fermions are anti-symmetric, then you can derive the Pauli Exclusion Principle. If you assume the Pauli Exclusion Principle, you can derive anti-symmetry in the wavefunction.

At some point, one of these must have been proved independently of the other. I can't seem to find such a proof anywhere. I think this confusion also comes from the fact that spin is a difficult thing to conceptualize, let alone measure. Does some experimental data to necessarily imply one of the two? I guess, some insight on how spin was discovered would probably help.