Theorem bnnlm

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

	Ref	Expression
Assertion	bnnlm	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmMod )

Proof

Step	Hyp	Ref	Expression
1		bnnvc	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmVec )
2		nvcnlm	⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod )
3	1 2	syl	⊢ ( 𝑊 ∈ Ban → 𝑊 ∈ NrmMod )