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