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Theorem con34b 285
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )

Proof of Theorem con34b
StepHypRef Expression
1 con3 128 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
2 ax-3 9 . 2  |-  ( ( -.  ps  ->  -.  ph )  ->  ( ph  ->  ps ) )
31, 2impbii 182 1  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178
This theorem is referenced by:  mtt  331  pm4.14  564  dfom2  4549  weniso  5704  dfsup2  7079  wemapso2lem  7149  pwfseqlem3  8162  indstr  10166  rpnnen2  12378  algcvgblem  12621  isirred2  15318  isdomn2  15872  ist0-3  16905  mdegleb  19282  dchrelbas4  20314  ltl4ev  24157  supnuf  24795  supexr  24797  raldifsni  25919  isdomn3  26689  conss34  26812
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179
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