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Metamath Proof Explorer

Theorem cmetmeti

Description: A complete metric space is a metric space. (Contributed by NM, 26-Oct-2007)

		Ref	Expression
	Hypothesis	cmetmeti.1	$⊢ D \in CMet (X)$
	Assertion	cmetmeti	$⊢ D \in Met (X)$

Step	Hyp	Ref	Expression
1		cmetmeti.1	$⊢ D \in CMet (X)$
2		cmetmet	$⊢ D \in CMet (X) \to D \in Met (X)$
3	1 2	ax-mp	$⊢ D \in Met (X)$