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Metamath Proof Explorer

Theorem rnblopn

Description: A ball of a metric space is an open set. (Contributed by NM, 12-Sep-2006)

		Ref	Expression
	Hypothesis	mopni.1	$⊢ J = MetOpen (D)$
	Assertion	rnblopn	$⊢ (D \in ∞Met (X) \land B \in ran ball (D)) \to B \in J$

Step	Hyp	Ref	Expression
1		mopni.1	$⊢ J = MetOpen (D)$
2	1	blssopn	$⊢ D \in ∞Met (X) \to ran ball (D) \subseteq J$
3	2	sselda	$⊢ (D \in ∞Met (X) \land B \in ran ball (D)) \to B \in J$