ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orel1 Unicode version

Theorem orel1 714
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
orel1  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )

Proof of Theorem orel1
StepHypRef Expression
1 pm2.53 711 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
21com12 30 1  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  biorf  733  pm2.25dc  878  pm2.85dc  890  euor2  2057  prel12  3698  funun  5167  acexmidlema  5765  acexmidlemb  5766  sup3exmid  8727
  Copyright terms: Public domain W3C validator