Theorem 3orel13

Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011)

	Ref	Expression
Assertion	3orel13	⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		3orel3	⊢ ( ¬ 𝜒 → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜓 ) ) )
2		orel1	⊢ ( ¬ 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )
3	1 2	sylan9r	⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → 𝜓 ) )