Theorem metxmet

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

	Ref	Expression
Assertion	metxmet	$$⊢D\in \mathrm{Met}\left(X\right)\to D\in \mathrm{\infty Met}\left(X\right)$$

Proof

Step	Hyp	Ref	Expression
1		ismet2	$$⊢D\in \mathrm{Met}\left(X\right)\leftrightarrow \left(D\in \mathrm{\infty Met}\left(X\right)\wedge D:X\times X⟶ℝ\right)$$
2	1	simplbi	$$⊢D\in \mathrm{Met}\left(X\right)\to D\in \mathrm{\infty Met}\left(X\right)$$