Theorem anidm

Description: Idempotent law for conjunction. (Contributed by NM, 8-Jan-2004) (Proof shortened by Wolf Lammen, 14-Mar-2014)

	Ref	Expression
Assertion	anidm	$$⊢\left(\phi \wedge \phi \right)\leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		pm4.24	$$⊢\phi \leftrightarrow \left(\phi \wedge \phi \right)$$
2	1	bicomi	$$⊢\left(\phi \wedge \phi \right)\leftrightarrow \phi$$