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

Theorem pm2.65i 640
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 627 . 2  |-  ( ph  ->  -.  ph )
4 pm2.01 617 . 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 615  ax-in2 616
This theorem is referenced by:  mt2  641  mto  663  pm5.19  707  noel  3441  0nelop  4269  elirr  4561  en2lp  4574  soirri  5044  canth  5853  0neqopab  5945  fzp1disj  10116  fzonel  10196  fzouzdisj  10216  4sqlem17  12450  lgsval2lem  14897  bj-imnimnn  14976  nnnotnotr  15228
  Copyright terms: Public domain W3C validator