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Theorem notnotnot 623
Description: Triple negation is equivalent to negation. (Contributed by Jim Kingdon, 28-Jul-2018.)
Assertion
Ref Expression
notnotnot (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)

Proof of Theorem notnotnot
StepHypRef Expression
1 notnot 618 . . 3 (𝜑 → ¬ ¬ 𝜑)
21con3i 621 . 2 (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3 notnot 618 . 2 𝜑 → ¬ ¬ ¬ 𝜑)
42, 3impbii 125 1 (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  stabnot  818  dcnnOLD  834  bj-nnsn  13050
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