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Theorem pm2.13dc 885
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 835 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 notnotrdc 843 . . . . 5  |-  (DECID  ph  ->  ( -.  -.  ph  ->  ph ) )
32con3d 631 . . . 4  |-  (DECID  ph  ->  ( -.  ph  ->  -.  -.  -.  ph ) )
43orim2d 788 . . 3  |-  (DECID  ph  ->  ( ( ph  \/  -.  ph )  ->  ( ph  \/  -.  -.  -.  ph ) ) )
51, 4biimtrid 152 . 2  |-  (DECID  ph  ->  (DECID  ph  ->  ( ph  \/  -.  -.  -.  ph ) ) )
65pm2.43i 49 1  |-  (DECID  ph  ->  (
ph  \/  -.  -.  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 708  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by: (None)
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