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Theorem notnotnot 615
Description: Triple negation. (Contributed by Jim Kingdon, 28-Jul-2018.)
Assertion
Ref Expression
notnotnot (¬ ¬ ¬ φ ↔ ¬ φ)

Proof of Theorem notnotnot
StepHypRef Expression
1 notnot1 547 . . 3 (φ → ¬ ¬ φ)
21con3i 549 . 2 (¬ ¬ ¬ φ → ¬ φ)
3 notnot1 547 . 2 φ → ¬ ¬ ¬ φ)
42, 3impbii 117 1 (¬ ¬ ¬ φ ↔ ¬ φ)
Colors of variables: wff set class
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 532  ax-in2 533
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  stabnot  729  testbitestn  732  dcnbidcnn  6359
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