Description: The scalar field of a topological vector space is a topological division ring. (Contributed by Mario Carneiro, 5-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | tlmtrg.f | |- F = ( Scalar ` W ) |
|
Assertion | tvctdrg | |- ( W e. TopVec -> F e. TopDRing ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tlmtrg.f | |- F = ( Scalar ` W ) |
|
2 | 1 | istvc | |- ( W e. TopVec <-> ( W e. TopMod /\ F e. TopDRing ) ) |
3 | 2 | simprbi | |- ( W e. TopVec -> F e. TopDRing ) |