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Metamath Proof Explorer

Theorem metxmet

Description: A metric is an extended metric. (Contributed by Mario Carneiro, 20-Aug-2015)

		Ref	Expression
	Assertion	metxmet	$⊢ D \in Met (X) \to D \in ∞Met (X)$

Step	Hyp	Ref	Expression
1		ismet2	$⊢ D \in Met (X) \leftrightarrow (D \in ∞Met (X) \land D : X \times X ⟶ ℝ)$
2	1	simplbi	$⊢ D \in Met (X) \to D \in ∞Met (X)$