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Theorem notnotrdc 829
 Description: Double negation elimination for a decidable proposition. The converse, notnot 619, holds for all propositions, not just decidable ones. This is Theorem *2.14 of [WhiteheadRussell] p. 102, but with a decidability condition added. (Contributed by Jim Kingdon, 11-Mar-2018.)
Assertion
Ref Expression
notnotrdc DECID

Proof of Theorem notnotrdc
StepHypRef Expression
1 df-dc 821 . . 3 DECID
2 orcom 718 . . 3
31, 2bitri 183 . 2 DECID
4 pm2.53 712 . 2
53, 4sylbi 120 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 698  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-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-dc 821 This theorem is referenced by:  dcstab  830  notnotbdc  858  condandc  867  pm2.13dc  871  pm2.54dc  877  mkvprop  7042
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