By proof, we know that Gödel's first Theorem applies to certain formal/axiomatic system, while the unprovable statement to which Gödel refers, the so-called "Gödel Sentence", is designed to refer, indirectly, to itself.
Question: Let every axiom of a formal/axiomatic system be a Gödel Sentence, referring indirectly to itself (including the primitive case of a formal system of only one axiom) then how would this implicate Gödel's proof of his first theorem?