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Theorem 2false 627
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 585 . 2  |-  ( ph  ->  ps )
3 2false.2 . . 3  |-  -.  ps
43pm2.21i 585 . 2  |-  ( ps 
->  ph )
52, 4impbii 121 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 104  ax-ia3 105  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  bianfi  865  bifal  1272  dfnul2  3253  dfnul3  3254  rab0  3273  iun0  3740  0iun  3741  0xp  4447  cnv0  4754  co02  4861  0er  6170  bdnth  10320  bdnthALT  10321
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