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Theorem pm2.1dc 822
Description: Commuted law of the excluded middle for a decidable proposition. Based on theorem *2.1 of [WhiteheadRussell] p. 101. (Contributed by Jim Kingdon, 25-Mar-2018.)
Assertion
Ref Expression
pm2.1dc  |-  (DECID  ph  ->  ( -.  ph  \/  ph )
)

Proof of Theorem pm2.1dc
StepHypRef Expression
1 df-dc 820 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 orcom 717 . . 3  |-  ( (
ph  \/  -.  ph )  <->  ( -.  ph  \/  ph )
)
31, 2bitri 183 . 2  |-  (DECID  ph  <->  ( -.  ph  \/  ph ) )
43biimpi 119 1  |-  (DECID  ph  ->  ( -.  ph  \/  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 697  DECID wdc 819
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-io 698
This theorem depends on definitions:  df-bi 116  df-dc 820
This theorem is referenced by:  pm2.6dc  847  rabrsndc  3586
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