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Metamath Proof Explorer

Theorem inidm

Description: Idempotent law for intersection of classes. Theorem 15 of Suppes p. 26. (Contributed by NM, 5-Aug-1993)

		Ref	Expression
	Assertion	inidm	$⊢ A \cap A = A$

Step	Hyp	Ref	Expression
1		anidm	$⊢ (x \in A \land x \in A) \leftrightarrow x \in A$
2	1	ineqri	$⊢ A \cap A = A$