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Theorem pm5.6dc 869
 Description: Conjunction in antecedent versus disjunction in consequent, for a decidable proposition. Theorem *5.6 of [WhiteheadRussell] p. 125, with decidability condition added. The reverse implication holds for all propositions (see pm5.6r 870). (Contributed by Jim Kingdon, 2-Apr-2018.)
Assertion
Ref Expression
pm5.6dc DECID

Proof of Theorem pm5.6dc
StepHypRef Expression
1 dfordc 825 . . 3 DECID
21imbi2d 228 . 2 DECID
3 impexp 259 . 2
42, 3syl6rbbr 197 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 102   wb 103   wo 662  DECID wdc 776 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663 This theorem depends on definitions:  df-bi 115  df-dc 777 This theorem is referenced by: (None)
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