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