ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.65d Unicode version

Theorem pm2.65d 650
Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994.) (Proof shortened by Wolf Lammen, 26-May-2013.)
Hypotheses
Ref Expression
pm2.65d.1  |-  ( ph  ->  ( ps  ->  ch ) )
pm2.65d.2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
Assertion
Ref Expression
pm2.65d  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.65d
StepHypRef Expression
1 pm2.65d.2 . . 3  |-  ( ph  ->  ( ps  ->  -.  ch ) )
2 pm2.65d.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2nsyld 638 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
43pm2.01d 608 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605
This theorem is referenced by:  pm2.65da  651  mtod  653
  Copyright terms: Public domain W3C validator