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

Theorem imdistanri 435
Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)
Hypothesis
Ref Expression
imdistanri.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
imdistanri  |-  ( ( ps  /\  ph )  ->  ( ch  /\  ph ) )

Proof of Theorem imdistanri
StepHypRef Expression
1 imdistanri.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21com12 30 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32impac 373 1  |-  ( ( ps  /\  ph )  ->  ( ch  /\  ph ) )
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 is referenced by: (None)
  Copyright terms: Public domain W3C validator