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Theorem pm2.68dc 827
Description: Concluding disjunction from implication for a decidable proposition. Based on theorem *2.68 of [WhiteheadRussell] p. 108. Converse of pm2.62 700 and one half of dfor2dc 828. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
pm2.68dc  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )

Proof of Theorem pm2.68dc
StepHypRef Expression
1 jarl 617 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( -.  ph  ->  ps ) )
2 pm2.54dc 824 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ph  \/  ps ) ) )
31, 2syl5 32 1  |-  (DECID  ph  ->  ( ( ( ph  ->  ps )  ->  ps )  ->  ( ph  \/  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ 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:  dfor2dc  828
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