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Theorem impcon4bid 198
Description: A variation on impbid 185 with contraposition. (Contributed by Jeff Hankins, 3-Jul-2009.)
Hypotheses
Ref Expression
impcon4bid.1  |-  ( ph  ->  ( ps  ->  ch ) )
impcon4bid.2  |-  ( ph  ->  ( -.  ps  ->  -. 
ch ) )
Assertion
Ref Expression
impcon4bid  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem impcon4bid
StepHypRef Expression
1 impcon4bid.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 impcon4bid.2 . . 3  |-  ( ph  ->  ( -.  ps  ->  -. 
ch ) )
32con4d 100 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3impbid 185 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 178
This theorem is referenced by:  con4bid  286  soisoi  6050  isomin  6059  alephdom  7964  nn0n0n1ge2b  10283  om2uzlt2i  11293  sadcaddlem  12971  isprm5  13114  pcdvdsb  13244
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 179
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