Theorem 3orcoma

Description: Commutation law for triple disjunction. (Contributed by Mario Carneiro, 4-Sep-2016)

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

Proof

Step	Hyp	Ref	Expression
1		or12	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\psi \vee \left(\phi \vee \chi \right)\right)$$
2		3orass	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
3		3orass	$$⊢\left(\psi \vee \phi \vee \chi \right)\leftrightarrow \left(\psi \vee \left(\phi \vee \chi \right)\right)$$
4	1 2 3	3bitr4i	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\psi \vee \phi \vee \chi \right)$$