Theorem 3orel3

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

	Ref	Expression
Assertion	3orel3	⊢ ( ¬ 𝜒 → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		df-3or	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )
2		orel2	⊢ ( ¬ 𝜒 → ( ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) → ( 𝜑 ∨ 𝜓 ) ) )
3	1 2	biimtrid	⊢ ( ¬ 𝜒 → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜓 ) ) )