Write PA for the theory Peano arithmetic, and Con(PA) for the statement of arithmetic that formalizes the claim "PA is consistent". Con(PA) could be of the form "For every natural number "n", "n" is not the Gödel number of a proof from PA that 0=1". (This formulation uses 0=1 instead of a direct contradiction; that gives the same result, because PA certainly proves ¬0=1, so if it proved 0=1 as well we would have a contradiction, and on the other hand, if PA proves a contradiction, then it proves anything, including 0=1.)