Metamath Proof Explorer


Theorem nvclmod

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

Ref Expression
Assertion nvclmod ( 𝑊 ∈ NrmVec → 𝑊 ∈ LMod )

Proof

Step Hyp Ref Expression
1 nvcnlm ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod )
2 nlmlmod ( 𝑊 ∈ NrmMod → 𝑊 ∈ LMod )
3 1 2 syl ( 𝑊 ∈ NrmVec → 𝑊 ∈ LMod )