ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  con3and Unicode version

Theorem con3and 564
Description: Variant of con3d 561 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
con3and.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
con3and  |-  ( (
ph  /\  -.  ch )  ->  -.  ps )

Proof of Theorem con3and
StepHypRef Expression
1 con3and.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21con3d 561 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
32imp 115 1  |-  ( (
ph  /\  -.  ch )  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-in1 544  ax-in2 545
This theorem is referenced by:  nelneq  2138  nelneq2  2139
  Copyright terms: Public domain W3C validator