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Theorem dfor2dc 881
Description: Disjunction 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 pm2.62 738 . 2  |-  ( (
ph  \/  ps )  ->  ( ( ph  ->  ps )  ->  ps )
)
2 pm2.68dc 880 . 2  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2impbid2 142 1  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( ( ph  ->  ps )  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    \/ wo 698  DECID wdc 820
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-dc 821
This theorem is referenced by:  imimorbdc  882
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