Theorem 3orcomb

Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011) (Proof shortened by Wolf Lammen, 8-Apr-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3orcoma	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\psi \vee \phi \vee \chi \right)$$
2		3orrot	$$⊢\left(\psi \vee \phi \vee \chi \right)\leftrightarrow \left(\phi \vee \chi \vee \psi \right)$$
3	1 2	bitri	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \chi \vee \psi \right)$$