Theorem nvcnlm

Description: A normed vector space is a normed module. (Contributed by Mario Carneiro, 4-Oct-2015)

	Ref	Expression
Assertion	nvcnlm	⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod )

Proof

Step	Hyp	Ref	Expression
1		isnvc	⊢ ( 𝑊 ∈ NrmVec ↔ ( 𝑊 ∈ NrmMod ∧ 𝑊 ∈ LVec ) )
2	1	simplbi	⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod )