Theorem rexmet

Description: The absolute value metric is an extended metric. (Contributed by Mario Carneiro, 28-Aug-2015)

	Ref	Expression
Hypothesis	remet.1	$$⊢D={\left(\mathrm{abs}\circ -\right)\upharpoonright }_{{ℝ}^2}$$
Assertion	rexmet	$$⊢D\in \mathrm{\infty Met}\left(ℝ\right)$$

Proof

Step	Hyp	Ref	Expression
1		remet.1	$$⊢D={\left(\mathrm{abs}\circ -\right)\upharpoonright }_{{ℝ}^2}$$
2	1	remet	$$⊢D\in \mathrm{Met}\left(ℝ\right)$$
3		metxmet	$$⊢D\in \mathrm{Met}\left(ℝ\right)\to D\in \mathrm{\infty Met}\left(ℝ\right)$$
4	2 3	ax-mp	$$⊢D\in \mathrm{\infty Met}\left(ℝ\right)$$