Theorem notnotnot 628

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		notnot 559	. . 3 ⊢ (𝜑 → ¬ ¬ 𝜑)
2	1	con3i 562	. 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3		notnot 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  741  testbitestn  823