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Theorem pm5.74rd 182
Description: Distribution of implication over biconditional (deduction form). (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 pm5.74 178 . 2  |-  ( ( ps  ->  ( ch  <->  th ) )  <->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
31, 2sylibr 133 1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm5.35  907
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