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Theorem con1b 334
Description: Contraposition. Bidirectional version of con1 131. (Contributed by NM, 3-Jan-1993.)
Assertion
Ref Expression
con1b  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)

Proof of Theorem con1b
StepHypRef Expression
1 con1 131 . 2  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) )
2 con1 131 . 2  |-  ( ( -.  ps  ->  ph )  ->  ( -.  ph  ->  ps ) )
31, 2impbii 190 1  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188
This theorem is referenced by:  eximal  1662  r19.23v  2912  pwssun  4760  ist1-2  20294  cmpfi  20354  dchrelbas2  24028
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