# Prove $\vdash \neg \neg A \leftrightarrow A$ in intuitionistic logic

I want to prove $\vdash \neg \neg A \leftrightarrow A$ without using $RAA$ and $\bot$ rules. the part that $\vdash A \to \neg \neg A$ is simple but I can't prove the other part. is there any possibility for proving $\vdash \neg \neg A \to A$ without using $RAA$ and $\bot$ rule in natural deduction?

• You cannot prove the "other part" because it is not intuitionistically valid. – Mauro ALLEGRANZA Nov 28 '16 at 14:26
• @MauroALLEGRANZA thank you – Karo Nov 28 '16 at 14:28
• See Intuitionistic Logic for the basic facts about it. – Mauro ALLEGRANZA Nov 28 '16 at 14:29