Metamath Proof Explorer


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 )