Prove that $A \leftrightarrow \lnot\lnot A$ (WIP)

Task

Prove that $A \leftrightarrow \lnot\lnot A$ using only the following axioms:

1. $P \rightarrow (Q \rightarrow P)$
2. $(P \rightarrow (Q \rightarrow R)) \rightarrow ((P \rightarrow Q) \rightarrow (P \rightarrow R))$
3. $(P \rightarrow Q) \leftrightarrow (\lnot Q \rightarrow \lnot P)$

Scoring

Your score will be the number of times you apply any of the axioms above.

posted about 3 years ago

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