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Theorem pm5.15dc 1367
 Description: A decidable proposition is equivalent to a decidable proposition or its negation. Based on theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 18-Apr-2018.)
Assertion
Ref Expression
pm5.15dc DECID DECID

Proof of Theorem pm5.15dc
StepHypRef Expression
1 xor3dc 1365 . . . . 5 DECID DECID
21imp 123 . . . 4 DECID DECID
32biimpd 143 . . 3 DECID DECID
4 dcbi 920 . . . . 5 DECID DECID DECID
54imp 123 . . . 4 DECID DECID DECID
6 dfordc 877 . . . 4 DECID
75, 6syl 14 . . 3 DECID DECID
83, 7mpbird 166 . 2 DECID DECID
98ex 114 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   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-in1 603  ax-in2 604  ax-io 698 This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820 This theorem is referenced by: (None)
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