Theorem oridm

Description: Idempotent law for disjunction. Theorem *4.25 of WhiteheadRussell p. 117. (Contributed by NM, 11-May-1993) (Proof shortened by Andrew Salmon, 16-Apr-2011) (Proof shortened by Wolf Lammen, 10-Mar-2013)

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

Proof

Step	Hyp	Ref	Expression
1		pm1.2	$$⊢\left(\phi \vee \phi \right)\to \phi$$
2		pm2.07	$$⊢\phi \to \left(\phi \vee \phi \right)$$
3	1 2	impbii	$$⊢\left(\phi \vee \phi \right)\leftrightarrow \phi$$