Description: A normed vector space is a normed module. (Contributed by Mario Carneiro, 4-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | nvcnlm | ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isnvc | ⊢ ( 𝑊 ∈ NrmVec ↔ ( 𝑊 ∈ NrmMod ∧ 𝑊 ∈ LVec ) ) | |
2 | 1 | simplbi | ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod ) |