Description: The scalar component of a left module is a normed group. (Contributed by Mario Carneiro, 4-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nlmnrg.1 | ⊢ 𝐹 = ( Scalar ‘ 𝑊 ) | |
Assertion | nlmngp2 | ⊢ ( 𝑊 ∈ NrmMod → 𝐹 ∈ NrmGrp ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nlmnrg.1 | ⊢ 𝐹 = ( Scalar ‘ 𝑊 ) | |
2 | 1 | nlmnrg | ⊢ ( 𝑊 ∈ NrmMod → 𝐹 ∈ NrmRing ) |
3 | nrgngp | ⊢ ( 𝐹 ∈ NrmRing → 𝐹 ∈ NrmGrp ) | |
4 | 2 3 | syl | ⊢ ( 𝑊 ∈ NrmMod → 𝐹 ∈ NrmGrp ) |