The corollary also indicates the epistemological relevance of the second incompleteness theorem. It would actually provide no interesting information if a system "F" proved its consistency. This is because inconsistent theories prove everything, including their consistency. Thus a consistency proof of "F" in "F" would give us no clue as to whether "F" really is consistent; no doubts about the consistency of "F" would be resolved by such a consistency proof. The interest in consistency proofs lies in the possibility of proving the consistency of a system "F" in some system "F’" that is in some sense less doubtful than "F" itself, for example weaker than "F". For many naturally occurring theories "F" and "F’", such as "F" = Zermelo–Fraenkel set theory and "F’" = primitive recursive arithmetic, the consistency of "F’" is provable in "F", and thus "F’" cannot prove the consistency of "F" by the above corollary of the second incompleteness theorem.