Theorem 3orass

Description: Associative law for triple disjunction. (Contributed by NM, 8-Apr-1994)

	Ref	Expression
Assertion	3orass	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$

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		orass	$$⊢\left(\left(\phi \vee \psi \right)\vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
3	1 2	bitri	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$