# Provability of NP /= P?

I'm a novice to the topic of provability so bear with me...

During a discussion with a friend, the question came up whether it could be possible that proving that $NP \neq P$ (or $NP = P$) is an unprovable statement. My friend opposed that, if indeed it was unprovable, then this would imply that there cannot be a polynomial time algorithm for NP-hard problems (as the existence of such proves the statement), thus implying $NP \neq P$. This seems to be imply that the statement cannot be unprovable or am I missing something?