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Theorem pm5.74rd 239
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 19-Mar-1997.)
Hypothesis
Ref Expression
pm5.74rd.1  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
Assertion
Ref Expression
pm5.74rd  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )

Proof of Theorem pm5.74rd
StepHypRef Expression
1 pm5.74rd.1 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
2 pm5.74 235 . 2  |-  ( ( ps  ->  ( ch  <->  th ) )  <->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
31, 2sylibr 203 1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  pm5.35  869
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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