Description: A normed vector space is a left module. (Contributed by Mario Carneiro, 4-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | nvclmod | ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ LMod ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nvcnlm | ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ NrmMod ) | |
2 | nlmlmod | ⊢ ( 𝑊 ∈ NrmMod → 𝑊 ∈ LMod ) | |
3 | 1 2 | syl | ⊢ ( 𝑊 ∈ NrmVec → 𝑊 ∈ LMod ) |