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Theorem pm2.26dc 847
Description: Decidable proposition version of theorem *2.26 of [WhiteheadRussell] p. 104. (Contributed by Jim Kingdon, 20-Apr-2018.)
Assertion
Ref Expression
pm2.26dc (DECID 𝜑 → (¬ 𝜑 ∨ ((𝜑𝜓) → 𝜓)))

Proof of Theorem pm2.26dc
StepHypRef Expression
1 pm2.27 39 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
2 imordc 830 . 2 (DECID 𝜑 → ((𝜑 → ((𝜑𝜓) → 𝜓)) ↔ (¬ 𝜑 ∨ ((𝜑𝜓) → 𝜓))))
31, 2mpbii 146 1 (DECID 𝜑 → (¬ 𝜑 ∨ ((𝜑𝜓) → 𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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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