ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  con2 Unicode version

Theorem con2 572
Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)
Assertion
Ref Expression
con2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )

Proof of Theorem con2
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ph  ->  -.  ps ) )
21con2d 554 1  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
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:  con2b  593
  Copyright terms: Public domain W3C validator