This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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