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

Theorem pm2.65i 639
Description: Inference for proof by contradiction. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)
Hypotheses
Ref Expression
pm2.65i.1  |-  ( ph  ->  ps )
pm2.65i.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
pm2.65i  |-  -.  ph

Proof of Theorem pm2.65i
StepHypRef Expression
1 pm2.65i.2 . . 3  |-  ( ph  ->  -.  ps )
2 pm2.65i.1 . . 3  |-  ( ph  ->  ps )
31, 2nsyl3 626 . 2  |-  ( ph  ->  -.  ph )
4 pm2.01 616 . 2  |-  ( (
ph  ->  -.  ph )  ->  -.  ph )
53, 4ax-mp 5 1  |-  -.  ph
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 614  ax-in2 615
This theorem is referenced by:  mt2  640  mto  662  pm5.19  706  noel  3426  0nelop  4248  elirr  4540  en2lp  4553  soirri  5023  canth  5828  0neqopab  5919  fzp1disj  10079  fzonel  10159  fzouzdisj  10179  lgsval2lem  14381  bj-imnimnn  14460  nnnotnotr  14712
  Copyright terms: Public domain W3C validator