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Theorem pm2.68dc 880
Description: Concluding disjunction from implication for a decidable proposition. Based on theorem *2.68 of [WhiteheadRussell] p. 108. Converse of pm2.62 738 and one half of dfor2dc 881. (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 648 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( -.  ph  ->  ps ) )
2 pm2.54dc 877 . 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 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:  dfor2dc  881
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