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Theorem notnotnot 661
Description: Triple negation. (Contributed by Jim Kingdon, 28-Jul-2018.)
Assertion
Ref Expression
notnotnot (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)

Proof of Theorem notnotnot
StepHypRef Expression
1 notnot 592 . . 3 (𝜑 → ¬ ¬ 𝜑)
21con3i 595 . 2 (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3 notnot 592 . 2 𝜑 → ¬ ¬ ¬ 𝜑)
42, 3impbii 124 1 (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  stabnot  775  testbitestn  857
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