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Theorem pm5.21 644
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.21  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)

Proof of Theorem pm5.21
StepHypRef Expression
1 simpl 107 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  -.  ph )
21pm2.21d 582 . 2  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  ->  ps ) )
3 simpr 108 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  -.  ps )
43pm2.21d 582 . 2  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ps  ->  ph ) )
52, 4impbid 127 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.21im  645
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