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Theorem pm2.521dc 798
Description: Theorem *2.521 of [WhiteheadRussell] p. 107, but with an additional decidability condition. (Contributed by Jim Kingdon, 5-May-2018.)
Assertion
Ref Expression
pm2.521dc (DECID 𝜑 → (¬ (𝜑𝜓) → (𝜓𝜑)))

Proof of Theorem pm2.521dc
StepHypRef Expression
1 pm2.52 615 . 2 (¬ (𝜑𝜓) → (¬ 𝜑 → ¬ 𝜓))
2 condc 783 . 2 (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))
31, 2syl5 32 1 (DECID 𝜑 → (¬ (𝜑𝜓) → (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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-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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