A theorem is a consequence of a set of axioms. By definition. It may be an a-priori truth in the context of the particular proof you are working on, but a-prio

A theorem is a consequence of a set of axioms. By definition. It may be an a-priori truth in the context of the particular proof you are working on, but a-priori your theorem there is always an axiom. Wanting to prove that X is a theorem of a-priori truth Y is the same thing as writing the algorithm for f: Y -> X