Theorem or12

Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993) (Proof shortened by Wolf Lammen, 14-Nov-2012)

	Ref	Expression
Assertion	or12	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\psi \vee \left(\phi \vee \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm1.5	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\to \left(\psi \vee \left(\phi \vee \chi \right)\right)$$
2		pm1.5	$$⊢\left(\psi \vee \left(\phi \vee \chi \right)\right)\to \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
3	1 2	impbii	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\psi \vee \left(\phi \vee \chi \right)\right)$$