I agree that if it’s possible, within a single logical framework F, to derive proposition P1 from proposition P2, then P1 is a theorem in F and not an axiom of F… or, at the very least, that it can be a theorem and need not be an axiom.
That said, if it’s possible in F to derive some prediction P3 from either P1 or P2, it does not follow that it’s possible to derive P1 from P2.
I agree that if it’s possible, within a single logical framework F, to derive proposition P1 from proposition P2, then P1 is a theorem in F and not an axiom of F… or, at the very least, that it can be a theorem and need not be an axiom.
That said, if it’s possible in F to derive some prediction P3 from either P1 or P2, it does not follow that it’s possible to derive P1 from P2.