Theorem pm2.26dc 892

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 ∨ ((𝜑 → 𝜓) → 𝜓)))

Proof of Theorem pm2.26dc

Step	Hyp	Ref	Expression
1		pm2.27 40	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
2		imordc 882	. 2 ⊢ (DECID 𝜑 → ((𝜑 → ((𝜑 → 𝜓) → 𝜓)) ↔ (¬ 𝜑 ∨ ((𝜑 → 𝜓) → 𝜓))))
3	1, 2	mpbii 147	1 ⊢ (DECID 𝜑 → (¬ 𝜑 ∨ ((𝜑 → 𝜓) → 𝜓)))

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-in1 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-dc 820

This theorem is referenced by: (None)