“证明这个定理”就是要证明这个蕴涵式是一个重言式。

To "prove the theorem" means to show that the implication is a tautology.

youdao

逻辑中的证明只是一种使得在复杂的情况下易于辨识重言式的机械的便利方法。

Proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases.

youdao

如果能证明该蕴涵式为重言式，那么其数学命题的证明推理形式就是正确的。

If the containing type can be proved to be heavy speech type, the method of the mathematical proposition proving and reasoning is correct.

youdao