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Theorem imdistand 443
Description: Distribution of implication with conjunction (deduction form). (Contributed by NM, 27-Aug-2004.)
Hypothesis
Ref Expression
imdistand.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
imdistand  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )

Proof of Theorem imdistand
StepHypRef Expression
1 imdistand.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 imdistan 440 . 2  |-  ( ( ps  ->  ( ch  ->  th ) )  <->  ( ( ps  /\  ch )  -> 
( ps  /\  th ) ) )
31, 2sylib 121 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
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:  imdistanda  444  pm5.32d  445  a2and  547  fconstfvm  5638  lbzbi  9420
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