Theorem notnotrALT 42149

Description: Converse of double negation. Alternate proof of notnotr 130. This proof is notnotrALTVD 42535 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
notnotrALT	⊢ (¬ ¬ 𝜑 → 𝜑)

Proof of Theorem notnotrALT

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (¬ ¬ 𝜑 → ¬ ¬ 𝜑)
2		pm2.21 123	. 2 ⊢ (¬ ¬ 𝜑 → (¬ 𝜑 → ¬ ¬ ¬ 𝜑))
3	1, 2	mt4d 117	1 ⊢ (¬ ¬ 𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)