I'm looking for a way to prove : $(A \rightarrow B) \rightarrow (\neg B \rightarrow \neg A)$
From the axioms :
A1) $(A) \rightarrow ( B \rightarrow A )$
A2) $(A \rightarrow ( B \rightarrow C )) \rightarrow((A\rightarrow B)\rightarrow(A\rightarrow C ))$
A3) $A \rightarrow (B \rightarrow (A \wedge B ))$
A4) $(A \wedge B )\rightarrow A$
A5) $(A \wedge B )\rightarrow B$
A6) $(A \rightarrow B )\rightarrow ((C \rightarrow B )\rightarrow ((A\vee C)\rightarrow B))$
A7) $A \rightarrow (A \vee B)$
A8) $A \rightarrow (B \vee A)$
A9) $ \neg \neg A \rightarrow A $
and MP
I'm studying in computer science and I don't know any think about logic course. Sorry for easy question and bad english.