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Theorem condcOLD 839
 Description: Obsolete proof of condc 838 as of 18-Nov-2023. (Contributed by Jim Kingdon, 13-Mar-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
condcOLD (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))

Proof of Theorem condcOLD
StepHypRef Expression
1 df-dc 820 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 ax-1 6 . . . 4 (𝜑 → (𝜓𝜑))
32a1d 22 . . 3 (𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))
4 pm2.27 40 . . . 4 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → ¬ 𝜓))
5 ax-in2 604 . . . 4 𝜓 → (𝜓𝜑))
64, 5syl6 33 . . 3 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))
73, 6jaoi 705 . 2 ((𝜑 ∨ ¬ 𝜑) → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))
81, 7sylbi 120 1 (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑)))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 697  DECID wdc 819 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698 This theorem depends on definitions:  df-bi 116  df-dc 820 This theorem is referenced by: (None)
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