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Theorem con1b 324
Description: Contraposition. Bidirectional version of con1 122. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con1b  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)

Proof of Theorem con1b
StepHypRef Expression
1 con1 122 . 2  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) )
2 con1 122 . 2  |-  ( ( -.  ps  ->  ph )  ->  ( -.  ph  ->  ps ) )
31, 2impbii 181 1  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177
This theorem is referenced by:  pwssun  4482  ist1-2  17404  cmpfi  17464  dchrelbas2  21014  xfree2  23941
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178
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