ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imdistand Unicode version

Theorem imdistand 436
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 433 . 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    /\ wa 102
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:  imdistanda  437  pm5.32d  438  fconstfvm  5431  lbzbi  8834
  Copyright terms: Public domain W3C validator