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Theorem 2false 690
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 635 . 2  |-  ( ph  ->  ps )
3 2false.2 . . 3  |-  -.  ps
43pm2.21i 635 . 2  |-  ( ps 
->  ph )
52, 4impbii 125 1  |-  ( ph  <->  ps )
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-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bianfi  931  bifal  1344  dfnul2  3360  dfnul3  3361  rab0  3386  iun0  3864  0iun  3865  0xp  4614  cnv0  4937  co02  5047  0er  6456  bdnth  13021  bdnthALT  13022
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