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Theorem 2false 702
Description: Two falsehoods are equivalent. (Contributed by NM, 4-Apr-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypotheses
Ref Expression
2false.1  |-  -.  ph
2false.2  |-  -.  ps
Assertion
Ref Expression
2false  |-  ( ph  <->  ps )

Proof of Theorem 2false
StepHypRef Expression
1 2false.1 . . 3  |-  -.  ph
21pm2.21i 647 . 2  |-  ( ph  ->  ps )
3 2false.2 . . 3  |-  -.  ps
43pm2.21i 647 . 2  |-  ( ps 
->  ph )
52, 4impbii 126 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in2 616
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  bianfi  948  bifal  1376  dfnul2  3438  dfnul3  3439  rab0  3465  iun0  3957  0iun  3958  0xp  4720  cnv0  5046  co02  5156  0er  6586  bdnth  14969  bdnthALT  14970
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