ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.68dc Unicode version

Theorem pm2.68dc 894
Description: Concluding disjunction from implication for a decidable proposition. Based on theorem *2.68 of [WhiteheadRussell] p. 108. Converse of pm2.62 748 and one half of dfor2dc 895. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
pm2.68dc  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )

Proof of Theorem pm2.68dc
StepHypRef Expression
1 jarl 658 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( -.  ph  ->  ps ) )
2 pm2.54dc 891 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2syl5 32 1  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 708  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by:  dfor2dc  895
  Copyright terms: Public domain W3C validator