ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfor2dc Unicode version

Theorem dfor2dc 794
Description: Logical 'or' expressed in terms of implication only, for a decidable proposition. Based on theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
dfor2dc  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( ( ph  ->  ps )  ->  ps )
) )

Proof of Theorem dfor2dc
StepHypRef Expression
1 pm2.62 667 . 2  |-  ( (
ph  \/  ps )  ->  ( ( ph  ->  ps )  ->  ps )
)
2 pm2.68dc 793 . 2  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2impbid2 131 1  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( ( ph  ->  ps )  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98    \/ wo 629  DECID wdc 742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by:  imimorbdc  795
  Copyright terms: Public domain W3C validator