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Theorem pm2.85dc 810
Description: Reverse distribution of disjunction over implication, given decidability. Based on theorem *2.85 of [WhiteheadRussell] p. 108. (Contributed by Jim Kingdon, 1-Apr-2018.)
Assertion
Ref Expression
pm2.85dc DECID

Proof of Theorem pm2.85dc
StepHypRef Expression
1 df-dc 742 . 2 DECID
2 orc 632 . . . 4
32a1d 22 . . 3
4 olc 631 . . . . . 6
54imim1i 54 . . . . 5
6 orel1 643 . . . . 5
75, 6syl9r 67 . . . 4
8 olc 631 . . . 4
97, 8syl6 29 . . 3
103, 9jaoi 635 . 2
111, 10sylbi 114 1 DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wo 628  DECID wdc 741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  orimdidc  811
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