Metamath Proof Explorer

Theorem nvclvec

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

Ref Expression
Assertion nvclvec ⊢ W ∈ NrmVec → W ∈ LVec

Proof

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