Theorem orcom

Description: Commutative law for disjunction. Theorem *4.31 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 15-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		pm1.4	$$⊢\left(\phi \vee \psi \right)\to \left(\psi \vee \phi \right)$$
2		pm1.4	$$⊢\left(\psi \vee \phi \right)\to \left(\phi \vee \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\psi \vee \phi \right)$$