Metamath Proof Explorer

Theorem tvctlm

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

Ref Expression
Assertion tvctlm 
|- ( W e. TopVec -> W e. TopMod )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  ( Scalar ` W ) = ( Scalar ` W )
2 1 istvc 
 |-  ( W e. TopVec <-> ( W e. TopMod /\ ( Scalar ` W ) e. TopDRing ) )
3 2 simplbi 
 |-  ( W e. TopVec -> W e. TopMod )