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Definition df-tvc 20831
Description: Define a topological left vector space, which is a topological module over a topological division ring. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
df-tvc  |-  TopVec  =  {
w  e. TopMod  |  (Scalar `  w )  e. TopDRing }

Detailed syntax breakdown of Definition df-tvc
StepHypRef Expression
1 ctvc 20827 . 2  class  TopVec
2 vw . . . . . 6  setvar  w
32cv 1397 . . . . 5  class  w
4 csca 14787 . . . . 5  class Scalar
53, 4cfv 5570 . . . 4  class  (Scalar `  w )
6 ctdrg 20825 . . . 4  class TopDRing
75, 6wcel 1823 . . 3  wff  (Scalar `  w )  e. TopDRing
8 ctlm 20826 . . 3  class TopMod
97, 2, 8crab 2808 . 2  class  { w  e. TopMod  |  (Scalar `  w
)  e. TopDRing }
101, 9wceq 1398 1  wff  TopVec  =  {
w  e. TopMod  |  (Scalar `  w )  e. TopDRing }
Colors of variables: wff setvar class
This definition is referenced by:  istvc  20860
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