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Theorem impcon4bid 208
Description: A variation on impbid 193 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 108 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3impbid 193 1  |-  ( ph  ->  ( ps  <->  ch )
)
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:  con4bid  294  soisoi  6234  isomin  6243  alephdom  8510  nn0n0n1ge2b  10933  om2uzlt2i  12162  sadcaddlem  14405  isprm5  14622  pcdvdsb  14781  cvgdvgrat  36302
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