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Theorem pm2.6dc 793
Description: Case elimination for a decidable proposition. Based on theorem *2.6 of [WhiteheadRussell] p. 107. (Contributed by Jim Kingdon, 25-Mar-2018.)
Assertion
Ref Expression
pm2.6dc  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ( ph  ->  ps )  ->  ps ) ) )

Proof of Theorem pm2.6dc
StepHypRef Expression
1 pm2.1dc 779 . . 3  |-  (DECID  ph  ->  ( -.  ph  \/  ph )
)
2 pm3.44 668 . . 3  |-  ( ( ( -.  ph  ->  ps )  /\  ( ph  ->  ps ) )  -> 
( ( -.  ph  \/  ph )  ->  ps ) )
31, 2syl5com 29 . 2  |-  (DECID  ph  ->  ( ( ( -.  ph  ->  ps )  /\  ( ph  ->  ps ) )  ->  ps ) )
43expd 254 1  |-  (DECID  ph  ->  ( ( -.  ph  ->  ps )  ->  ( ( ph  ->  ps )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    \/ 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-io 663
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by:  jadc  794  jaddc  795  pm2.61dc  796
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