ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.25dc Unicode version

Theorem pm2.25dc 830
Description: Elimination of disjunction based on a disjunction, for a decidable proposition. Based on theorem *2.25 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.25dc  |-  (DECID  ph  ->  (
ph  \/  ( ( ph  \/  ps )  ->  ps ) ) )

Proof of Theorem pm2.25dc
StepHypRef Expression
1 df-dc 781 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 orel1 679 . . 3  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )
32orim2i 713 . 2  |-  ( (
ph  \/  -.  ph )  ->  ( ph  \/  (
( ph  \/  ps )  ->  ps ) ) )
41, 3sylbi 119 1  |-  (DECID  ph  ->  (
ph  \/  ( ( ph  \/  ps )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 664  DECID wdc 780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator