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Theorem con1b 348
Description: Contraposition. Bidirectional version of con1 143. (Contributed by NM, 3-Jan-1993.)
Assertion
Ref Expression
con1b |- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )
Proof of Theorem con1b
StepHypRef Expression
1 con1 143 . 2 |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) )
2 con1 143 . 2 |- ( ( -. ps -> ph ) -> ( -. ph -> ps ) )
31, 2impbii 199 1 |- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4   <-> wb 196
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 197
This theorem is referenced by:  eximal  1707  r19.23v  3023  pwssun  5020  ist1-2  21151  cmpfi  21211  dchrelbas2  24962
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