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	$$⊢\neg \chi \to \left(\left(\phi \vee \psi \vee \chi \right)\to \left(\phi \vee \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-3or	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\vee \chi \right)$$
2		orel2	$$⊢\neg \chi \to \left(\left(\left(\phi \vee \psi \right)\vee \chi \right)\to \left(\phi \vee \psi \right)\right)$$
3	1 2	syl5bi	$$⊢\neg \chi \to \left(\left(\phi \vee \psi \vee \chi \right)\to \left(\phi \vee \psi \right)\right)$$