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Theorem notnotbdc 858
 Description: Double negation equivalence for a decidable proposition. Like Theorem *4.13 of [WhiteheadRussell] p. 117, but with a decidability antecendent. The forward direction, notnot 619, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 13-Mar-2018.)
Assertion
Ref Expression
notnotbdc DECID

Proof of Theorem notnotbdc
StepHypRef Expression
1 notnot 619 . 2
2 notnotrdc 829 . 2 DECID
31, 2impbid2 142 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104  DECID wdc 820 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 604  ax-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-dc 821 This theorem is referenced by:  con1biidc  863  imordc  883  dfbi3dc  1376  alexdc  1596
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