Wikipedia writes that in every consistent formal system that satisfies Gödel's first incompleteness theorem there exist statements about natural numbers that are true, but that are unprovable within the system. Let $B$ be such a statement.
Now, there are statements that imply other statements, for example, the Taniyama-Shimura conjecture implies Fermat's Last Theorem.$^1$
Let $A$ be a statement that implies $B$.
My question is: Since $B$ is unprovable, can $A$ possibly still be proven?
From what I understand, it shouldn't, because that would prove $B$ by implying it, but it is unprovable. But I am not entirely sure.
$^1$ Hoffman, P. (1999). The man who loved only numbers : the story of Paul Erdős and the search for mathematical truth (p. 196). Fourth Estate