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Theorem pm4.64dc 839
Description: Theorem *4.64 of [WhiteheadRussell] p. 120, given a decidability condition. The reverse direction, pm2.53 676, holds for all propositions. (Contributed by Jim Kingdon, 2-May-2018.)
Assertion
Ref Expression
pm4.64dc  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  <->  ( ph  \/  ps ) ) )

Proof of Theorem pm4.64dc
StepHypRef Expression
1 dfordc 829 . 2  |-  (DECID  ph  ->  ( ( ph  \/  ps ) 
<->  ( -.  ph  ->  ps ) ) )
21bicomd 139 1  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  <->  ( ph  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103    \/ wo 664  DECID wdc 780
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 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by:  pm4.66dc  840
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