I know there are plenty of similar posts around, but I could not find an answer to this particular question (and I've been at it for two days now, getting nowhere). The proof I'm trying to construe in Hilbert style system is:
$A \rightarrow (B \rightarrow C) \vdash B \rightarrow (A \rightarrow C)$.
Axioms given:
A1: $(A \rightarrow (B \rightarrow A))$;
A2: $((A \rightarrow(B\rightarrow C))\rightarrow ((A \rightarrow B) \rightarrow (A \rightarrow C)))$;
A3: $((\neg B \rightarrow \neg A) \rightarrow ((\neg B \rightarrow A) \rightarrow B))$.
This is the third exercise of Mendelson's book Introduction to Mathematical Logic. This is not for a class; I'm going through the book again, after having discussed many of its topics previously (but never having been required to do Hilbert proofs—luckily). Please don't give an answer which gives a proof in another proof system along with the equivalence of that with a Hilbert style system; I'm trying to be able to do Hilbert proofs. Thanks in advance!