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 ∨ ((𝜑 → 𝜓) → 𝜓)))

Proof of Theorem pm2.26dc

Step	Hyp	Ref	Expression
1		pm2.27 39	. 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
2		imordc 830	. 2 ⊢ (DECID 𝜑 → ((𝜑 → ((𝜑 → 𝜓) → 𝜓)) ↔ (¬ 𝜑 ∨ ((𝜑 → 𝜓) → 𝜓))))
3	1, 2	mpbii 146	1 ⊢ (DECID 𝜑 → (¬ 𝜑 ∨ ((𝜑 → 𝜓) → 𝜓)))

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)