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Theorem dfordc 825
Description: Definition of 'or' in terms of negation and implication for a decidable proposition. Based on definition of [Margaris] p. 49. One direction, pm2.53 674, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 26-Mar-2018.)
Assertion
Ref Expression
dfordc  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( -.  ph  ->  ps ) ) )

Proof of Theorem dfordc
StepHypRef Expression
1 pm2.53 674 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
2 pm2.54dc 824 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2impbid2 141 1  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( -.  ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103    \/ wo 662  DECID wdc 776
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-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by:  imordc  830  pm4.64dc  835  pm5.17dc  844  pm5.6dc  869  pm3.12dc  900  pm5.15dc  1321  19.32dc  1610  r19.32vdc  2508  prime  8579  isprm4  10708  prm2orodd  10715  euclemma  10732  phiprmpw  10805
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