Theorem 3orel1 1089

Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)

Assertion

Ref	Expression
3orel1	⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒)))

Proof of Theorem 3orel1

Step	Hyp	Ref	Expression
1		3orass 1088	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		orel1 885	. 2 ⊢ (¬ 𝜑 → ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ 𝜒)))
3	1, 2	syl5bi 241	1 ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843   ∨ w3o 1084

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 844  df-3or 1086

This theorem is referenced by:  3orel2  33556