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Theorem dfordc 860
Description: Definition of disjunction in terms of negation and implication for a decidable proposition. Based on definition of [Margaris] p. 49. One direction, pm2.53 694, 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 pm2.53 694 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
2 pm2.54dc 859 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2impbid2 142 1  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( -.  ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104    \/ wo 680  DECID wdc 802
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-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-dc 803
This theorem is referenced by:  imordc  865  pm4.64dc  868  pm5.17dc  872  pm5.6dc  894  pm3.12dc  925  pm5.15dc  1350  19.32dc  1640  r19.32vdc  2555  prime  9104  isprm4  11707  prm2orodd  11714  euclemma  11731  phiprmpw  11804
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