Godel's theorem as it appeared in Proposition VI of his 1931 paper "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I.":
To every w-consistent recursive class k of formulae there correspond recursive class-sings r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(k) (where v is the free variable of r).
which translates to
All consistent axiomatic formulations of number theory include undecidable propositions.
Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.