Theorem 3orel2OLD 1516

Description: Obsolete version of 3orel2 1515 as of 8-Oct-2025. (Contributed by Scott Fenton, 26-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
3orel2OLD	⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒)))

Proof of Theorem 3orel2OLD

Step	Hyp	Ref	Expression
1		3orrot 1108	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
2		3orel1 1107	. . 3 ⊢ (¬ 𝜓 → ((𝜓 ∨ 𝜒 ∨ 𝜑) → (𝜒 ∨ 𝜑)))
3		orcom 884	. . 3 ⊢ ((𝜒 ∨ 𝜑) ↔ (𝜑 ∨ 𝜒))
4	2, 3	imbitrdi 254	. 2 ⊢ (¬ 𝜓 → ((𝜓 ∨ 𝜒 ∨ 𝜑) → (𝜑 ∨ 𝜒)))
5	1, 4	biimtrid 245	1 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by: (None)