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 e. TopVec -> W e. LMod )

Proof

Step Hyp Ref Expression
1 tvctlm 
 |-  ( W e. TopVec -> W e. TopMod )
2 tlmlmod 
 |-  ( W e. TopMod -> W e. LMod )
3 1 2 syl 
 |-  ( W e. TopVec -> W e. LMod )