Theorem cnxmet

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

	Ref	Expression
Assertion	cnxmet	$$⊢\mathrm{abs}\circ -\in \mathrm{\infty Met}\left(ℂ\right)$$

Proof

Step	Hyp	Ref	Expression
1		cnmet	$$⊢\mathrm{abs}\circ -\in \mathrm{Met}\left(ℂ\right)$$
2		metxmet	$$⊢\mathrm{abs}\circ -\in \mathrm{Met}\left(ℂ\right)\to \mathrm{abs}\circ -\in \mathrm{\infty Met}\left(ℂ\right)$$
3	1 2	ax-mp	$$⊢\mathrm{abs}\circ -\in \mathrm{\infty Met}\left(ℂ\right)$$