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