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Theorem pm5.12dc 815
Description: Excluded middle with antecedents for a decidable consequent. Based on theorem *5.12 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.12dc DECID

Proof of Theorem pm5.12dc
StepHypRef Expression
1 df-dc 742 . 2 DECID
2 ax-1 5 . . 3
3 ax-1 5 . . 3
42, 3orim12i 675 . 2
51, 4sylbi 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-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
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