MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-tvc Structured version   Unicode version

Definition df-tvc 19872
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 19868 . 2  class  TopVec
2 vw . . . . . 6  setvar  w
32cv 1369 . . . . 5  class  w
4 csca 14363 . . . . 5  class Scalar
53, 4cfv 5529 . . . 4  class  (Scalar `  w )
6 ctdrg 19866 . . . 4  class TopDRing
75, 6wcel 1758 . . 3  wff  (Scalar `  w )  e. TopDRing
8 ctlm 19867 . . 3  class TopMod
97, 2, 8crab 2803 . 2  class  { w  e. TopMod  |  (Scalar `  w
)  e. TopDRing }
101, 9wceq 1370 1  wff  TopVec  =  {
w  e. TopMod  |  (Scalar `  w )  e. TopDRing }
Colors of variables: wff setvar class
This definition is referenced by:  istvc  19901
  Copyright terms: Public domain W3C validator