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Theorem impcon4bid 205
Description: A variation on impbid 191 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 105 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3impbid 191 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184
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 185
This theorem is referenced by:  con4bid  293  soisoi  6121  isomin  6130  alephdom  8355  nn0n0n1ge2b  10748  om2uzlt2i  11884  sadcaddlem  13764  isprm5  13909  pcdvdsb  14046
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