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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  |-  ( -. 
-.  -.  ph  <->  -.  ph )

Proof of Theorem notnotnot
StepHypRef Expression
1 notnot 618 . . 3  |-  ( ph  ->  -.  -.  ph )
21con3i 621 . 2  |-  ( -. 
-.  -.  ph  ->  -.  ph )
3 notnot 618 . 2  |-  ( -. 
ph  ->  -.  -.  -.  ph )
42, 3impbii 125 1  |-  ( -. 
-.  -.  ph  <->  -.  ph )
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  12930
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