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Theorem pm2.13dc 817
Description: A decidable proposition or its triple negation is true. Theorem *2.13 of [WhiteheadRussell] p. 101 with decidability condition added. (Contributed by Jim Kingdon, 13-May-2018.)
Assertion
Ref Expression
pm2.13dc  |-  (DECID  ph  ->  (
ph  \/  -.  -.  -.  ph ) )

Proof of Theorem pm2.13dc
StepHypRef Expression
1 df-dc 781 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 notnotrdc 789 . . . . 5  |-  (DECID  ph  ->  ( -.  -.  ph  ->  ph ) )
32con3d 596 . . . 4  |-  (DECID  ph  ->  ( -.  ph  ->  -.  -.  -.  ph ) )
43orim2d 737 . . 3  |-  (DECID  ph  ->  ( ( ph  \/  -.  ph )  ->  ( ph  \/  -.  -.  -.  ph ) ) )
51, 4syl5bi 150 . 2  |-  (DECID  ph  ->  (DECID  ph  ->  ( ph  \/  -.  -.  -.  ph ) ) )
65pm2.43i 48 1  |-  (DECID  ph  ->  (
ph  \/  -.  -.  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 664  DECID wdc 780
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 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by: (None)
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