In 1938 Gödel proved the consistency of the CH with ZFC. Assuming that ZF is consistent, he built a model of ZFC, known as the constructible universe, in which the CH holds. Thus, the proof shows that if ZF is consistent, then so is ZF together with the AC and the CH. Hence, assuming ZF is consistent, the AC cannot be disproved in ZF and the CH cannot be disproved in ZFC.