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Metamath Proof Explorer

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	$⊢ (φ \land φ) \leftrightarrow φ$

Step	Hyp	Ref	Expression
1		pm4.24	$⊢ φ \leftrightarrow (φ \land φ)$
2	1	bicomi	$⊢ (φ \land φ) \leftrightarrow φ$