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Theorem impcon4bid 196
Description: A variation on impbid 183 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 97 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3impbid 183 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  con4bid  284  soisoi  5841  isomin  5850  alephdom  7724  om2uzlt2i  11030  isprm5  12807  pcdvdsb  12937
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 177
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