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

Theorem pm2.65da 597
Description: Deduction rule for proof by contradiction. (Contributed by NM, 12-Jun-2014.)
Hypotheses
Ref Expression
pm2.65da.1  |-  ( (
ph  /\  ps )  ->  ch )
pm2.65da.2  |-  ( (
ph  /\  ps )  ->  -.  ch )
Assertion
Ref Expression
pm2.65da  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.65da
StepHypRef Expression
1 pm2.65da.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
21ex 112 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 pm2.65da.2 . . 3  |-  ( (
ph  /\  ps )  ->  -.  ch )
43ex 112 . 2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
52, 4pm2.65d 596 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem is referenced by:  condandc  786  nelrdva  2769  frirrg  4115  prodgt0  7893  ixxdisj  8873  icodisj  8961  ltabs  9914  divalglemnqt  10232
  Copyright terms: Public domain W3C validator