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Theorem imdistand 674
Description: Distribution of implication with conjunction (deduction rule). (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 671 . 2  |-  ( ( ps  ->  ( ch  ->  th ) )  <->  ( ( ps  /\  ch )  -> 
( ps  /\  th ) ) )
31, 2sylib 189 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  imdistanda  675  fconstfv  5954  unblem1  7359  cfub  8129  lbzbi  10564  predpo  25459  ispridl2  26648  ispridlc  26680  lnr2i  27297  usgra2pthspth  28305
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 178  df-an 361
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