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Metamath Proof Explorer

Theorem isnvc

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

Ref Expression
Assertion isnvc ⊢ W ∈ NrmVec ↔ W ∈ NrmMod ∧ W ∈ LVec

Proof

Step Hyp Ref Expression
1 df-nvc ⊢ NrmVec = NrmMod ∩ LVec
2 1 elin2 ⊢ W ∈ NrmVec ↔ W ∈ NrmMod ∧ W ∈ LVec