Theorem 3orel1

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

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

Proof

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