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Theorem pm5.74d 180
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)
Hypothesis
Ref Expression
pm5.74d.1  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
Assertion
Ref Expression
pm5.74d  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )

Proof of Theorem pm5.74d
StepHypRef Expression
1 pm5.74d.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
2 pm5.74 177 . 2  |-  ( ( ps  ->  ( ch  <->  th ) )  <->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
31, 2sylib 120 1  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  imbi2d  228  imim21b  250  pm5.74da  432  cbval2  1838  dfiin2g  3719  brecop  6262  dom2lem  6319  nn0ind-raph  8545
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