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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 )