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Theorem pm5.14dc 879
Description: A decidable proposition is implied by or implies other propositions. Based on theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.14dc  |-  (DECID  ps  ->  ( ( ph  ->  ps )  \/  ( ps  ->  ch ) ) )

Proof of Theorem pm5.14dc
StepHypRef Expression
1 df-dc 803 . 2  |-  (DECID  ps  <->  ( ps  \/  -.  ps ) )
2 ax-1 6 . . 3  |-  ( ps 
->  ( ph  ->  ps ) )
3 ax-in2 587 . . 3  |-  ( -. 
ps  ->  ( ps  ->  ch ) )
42, 3orim12i 731 . 2  |-  ( ( ps  \/  -.  ps )  ->  ( ( ph  ->  ps )  \/  ( ps  ->  ch ) ) )
51, 4sylbi 120 1  |-  (DECID  ps  ->  ( ( ph  ->  ps )  \/  ( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 680  DECID wdc 802
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-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-dc 803
This theorem is referenced by:  pm5.13dc  880
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