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Theorem imdistand 692
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 689 . 2  |-  ( ( ps  ->  ( ch  ->  th ) )  <->  ( ( ps  /\  ch )  -> 
( ps  /\  th ) ) )
31, 2sylib 196 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( ps 
/\  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  imdistanda  693  a2and  809  fconstfv  6122  unblem1  7771  cfub  8628  lbzbi  11169  predpo  28857  ispridl2  30054  ispridlc  30086  lnr2i  30685  usgra2pthspth  31834
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