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

Theorem jc 580
Description: Inference joining the consequents of two premises. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jc.1  |-  ( ph  ->  ps )
jc.2  |-  ( ph  ->  ch )
Assertion
Ref Expression
jc  |-  ( ph  ->  -.  ( ps  ->  -. 
ch ) )

Proof of Theorem jc
StepHypRef Expression
1 jc.1 . 2  |-  ( ph  ->  ps )
2 jc.2 . 2  |-  ( ph  ->  ch )
3 pm3.2im 566 . 2  |-  ( ps 
->  ( ch  ->  -.  ( ps  ->  -.  ch ) ) )
41, 2, 3sylc 56 1  |-  ( ph  ->  -.  ( ps  ->  -. 
ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator