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Theorem anordc 941
 Description: Conjunction in terms of disjunction (DeMorgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120, but where the propositions are decidable. The forward direction, pm3.1 744, holds for all propositions, but the equivalence only holds given decidability. (Contributed by Jim Kingdon, 21-Apr-2018.)
Assertion
Ref Expression
anordc DECID DECID

Proof of Theorem anordc
StepHypRef Expression
1 dcan 919 . 2 DECID DECID DECID
2 ianordc 885 . . . . 5 DECID
32bicomd 140 . . . 4 DECID
43a1d 22 . . 3 DECID DECID
54con2biddc 866 . 2 DECID DECID
61, 5syld 45 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   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-in1 604  ax-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821 This theorem is referenced by:  pm3.11dc  942  dn1dc  945
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