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Theorem pm2.68dc 831
Description: Concluding disjunction from implication for a decidable proposition. Based on theorem *2.68 of [WhiteheadRussell] p. 108. Converse of pm2.62 702 and one half of dfor2dc 832. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
pm2.68dc (DECID 𝜑 → (((𝜑𝜓) → 𝜓) → (𝜑𝜓)))

Proof of Theorem pm2.68dc
StepHypRef Expression
1 jarl 619 . 2 (((𝜑𝜓) → 𝜓) → (¬ 𝜑𝜓))
2 pm2.54dc 828 . 2 (DECID 𝜑 → ((¬ 𝜑𝜓) → (𝜑𝜓)))
31, 2syl5 32 1 (DECID 𝜑 → (((𝜑𝜓) → 𝜓) → (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 664  DECID wdc 780
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 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by:  dfor2dc  832
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