Theorem 3orrot

Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995)

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

Proof

Step	Hyp	Ref	Expression
1		orcom	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\left(\psi \vee \chi \right)\vee \phi \right)$$
2		3orass	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
3		df-3or	$$⊢\left(\psi \vee \chi \vee \phi \right)\leftrightarrow \left(\left(\psi \vee \chi \right)\vee \phi \right)$$
4	1 2 3	3bitr4i	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\psi \vee \chi \vee \phi \right)$$