Theorem ngpxms

Description: A normed group is an extended metric space. (Contributed by Mario Carneiro, 2-Oct-2015)

	Ref	Expression
Assertion	ngpxms	⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ ∞MetSp )

Proof

Step	Hyp	Ref	Expression
1		ngpms	⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ MetSp )
2		msxms	⊢ ( 𝐺 ∈ MetSp → 𝐺 ∈ ∞MetSp )
3	1 2	syl	⊢ ( 𝐺 ∈ NrmGrp → 𝐺 ∈ ∞MetSp )