Aquinas was a pretty competent logician, even if he was rather encumbered by a love of Aristotle. It's not the mechanics of proof*; it's the initial axioms.

* well, alright, perhaps it is, rather. I've heard a few "you can't do X from first principles" which often turns out to be a declaration that the speaker has a fairly broken notion of what it is to "do X" (that neatly complements their wrong set of first principles) rather than a tautology.