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Theorem pm5.74ri 237
Description: Distribution of implication over biconditional (reverse inference rule). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74ri.1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )
Assertion
Ref Expression
pm5.74ri  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem pm5.74ri
StepHypRef Expression
1 pm5.74ri.1 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )
2 pm5.74 235 . 2  |-  ( (
ph  ->  ( ps  <->  ch )
)  <->  ( ( ph  ->  ps )  <->  ( ph  ->  ch ) ) )
31, 2mpbir 200 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  bitrd  244  bibi2d  309  tbt  333  sbco2d  2040  2mos  2235  axgroth6  8466  isprm2  12782  ufileu  17630  sbco2dwAUX7  29560  sbco2dOLD7  29707
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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