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Prove that $\beta \rightarrow \neg \neg \beta$ is a theorem using standard axioms 1,2,3 and MP
I need to prove $p \rightarrow \neg \neg p$
My question is very similar to this, but with some differences. Axiom 3 that I'm using is different (though I've heard is equivalent) and the ONLY things I am allowed to use are the following three axioms, MP, and the Deduction Theorem:
A1: $A \rightarrow (B \rightarrow A)$
A2: $(A \rightarrow (B \rightarrow C)) \rightarrow ((A \rightarrow B) \rightarrow (A \rightarrow C))$
A3: $(\neg A \rightarrow \neg B) \rightarrow (B \rightarrow A)$
If another theorem/axiom is needed to solve this, it must be proven in-line of the main question. You cannot prove the extra theorem on the side and then use it in the proof.