Löb's theorem states that "If it's provable that (if it's provable that p then p), then it's provable that p." In addition to being a theorem of set theory with Peano arithmetic, it's also a theorem of modal logic.

Try this on for size: If I believe that (if I believe that this chocolate chip will cure my headache, then this chocolate chip will cure my headache), then I believe that this chocolate chip will cure my headache.

-Agenty Duck