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Metamath Proof Explorer

Theorem bln0

Description: A ball is not empty. (Contributed by NM, 6-Oct-2007) (Revised by Mario Carneiro, 12-Nov-2013)

		Ref	Expression
	Assertion	bln0	$⊢ (D \in ∞Met (X) \land P \in X \land R \in ℝ^{+}) \to P ball (D) R \neq \emptyset$

Step	Hyp	Ref	Expression
1		blcntr	$⊢ (D \in ∞Met (X) \land P \in X \land R \in ℝ^{+}) \to P \in (P ball (D) R)$
2	1	ne0d	$⊢ (D \in ∞Met (X) \land P \in X \land R \in ℝ^{+}) \to P ball (D) R \neq \emptyset$