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Theorem pm5.74da 432
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 4-May-2007.)
Hypothesis
Ref Expression
pm5.74da.1  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
Assertion
Ref Expression
pm5.74da  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )

Proof of Theorem pm5.74da
StepHypRef Expression
1 pm5.74da.1 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  <->  th )
)
21ex 113 . 2  |-  ( ph  ->  ( ps  ->  ( ch 
<->  th ) ) )
32pm5.74d 180 1  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> 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:  ralbida  2368  elrab3t  2758  dff13  5487  isprm3  10880
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