What can we say about a fixed point for a provability predicate in deductively defined theory that satisfies diagonalisation lemma
The formula $A$ is provable, this is almost exactly the content of Löb's Theorem.

The proof (which can be found on the Wikipedia page) is a bit contorted, as it requires an additional application of diagonalization to build and analyze the formula:

$$ \Psi \equiv Pr(\lceil\Psi\rceil)\rightarrow A $$