Metamath Proof Explorer

Theorem tvclmod

Description: A topological vector space is a left module. (Contributed by Mario Carneiro, 5-Oct-2015)

Ref Expression
Assertion tvclmod ⊢ W ∈ TopVec → W ∈ LMod

Proof

Step Hyp Ref Expression
1 tvctlm ⊢ W ∈ TopVec → W ∈ TopMod
2 tlmlmod ⊢ W ∈ TopMod → W ∈ LMod
3 1 2 syl ⊢ W ∈ TopVec → W ∈ LMod