Let M be a proof-checking Turing machine which takes two inputs, A and B. :
M(A,B) = 0 if A codes a valid proof of the sentence coded by B in ZFC.
M(A,B) = 1 if A does not code a valid proof of the sentence coded by B in ZFC.
Let M' be a provability-checking Turing machine which takes input B. :
M'(B) = 0 if B is provable in ZFC.
M'(B) does not terminate if B is not provable in ZFC.
My question: If M(X,B) = 0 then, M'(X) = 0 always?
It means, a valid proof is always provable?