Theorem notnotnot 627

Description: Triple negation. (Contributed by Jim Kingdon, 28-Jul-2018.)

Assertion

Ref	Expression
notnotnot	⊢ (¬ ¬ ¬ φ ↔ ¬ φ)

Proof of Theorem notnotnot

Step	Hyp	Ref	Expression
1		notnot1 559	. . 3 ⊢ (φ → ¬ ¬ φ)
2	1	con3i 561	. 2 ⊢ (¬ ¬ ¬ φ → ¬ φ)
3		notnot1 559	. 2 ⊢ (¬ φ → ¬ ¬ ¬ φ)
4	2, 3	impbii 117	1 ⊢ (¬ ¬ ¬ φ ↔ ¬ φ)

Syntax hints:  ¬ wn 3   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  stabnot  740  testbitestn  822