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Theorem pm2.6dc 759
 Description: Case elimination for a decidable proposition. Based on theorem *2.6 of [WhiteheadRussell] p. 107. (Contributed by Jim Kingdon, 25-Mar-2018.)
Assertion
Ref Expression
pm2.6dc (DECID 𝜑 → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓)))

Proof of Theorem pm2.6dc
StepHypRef Expression
1 pm2.1dc 745 . . 3 (DECID 𝜑 → (¬ 𝜑𝜑))
2 pm3.44 635 . . 3 (((¬ 𝜑𝜓) ∧ (𝜑𝜓)) → ((¬ 𝜑𝜑) → 𝜓))
31, 2syl5com 26 . 2 (DECID 𝜑 → (((¬ 𝜑𝜓) ∧ (𝜑𝜓)) → 𝜓))
43expd 245 1 (DECID 𝜑 → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓)))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97   ∨ wo 629  DECID wdc 742 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 630 This theorem depends on definitions:  df-bi 110  df-dc 743 This theorem is referenced by:  jadc  760  jaddc  761  pm2.61dc  762
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