Theorem bnngp

Description: A Banach space is a normed group. (Contributed by Mario Carneiro, 15-Oct-2015)

	Ref	Expression
Assertion	bnngp	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmGrp )

Proof

Step	Hyp	Ref	Expression
1		bnnlm	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmMod )
2		nlmngp	⊢ ( 𝑊 ∈ NrmMod → 𝑊 ∈ NrmGrp )
3	1 2	syl	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmGrp )