Definition df-tvc 22774

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 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}

Detailed syntax breakdown of Definition df-tvc

Step	Hyp	Ref	Expression
1		ctvc 22770	. 2 class TopVec
2		vw	. . . . . 6 setvar 𝑤
3	2	cv 1535	. . . . 5 class 𝑤
4		csca 16571	. . . . 5 class Scalar
5	3, 4	cfv 6358	. . . 4 class (Scalar‘𝑤)
6		ctdrg 22768	. . . 4 class TopDRing
7	5, 6	wcel 2113	. . 3 wff (Scalar‘𝑤) ∈ TopDRing
8		ctlm 22769	. . 3 class TopMod
9	7, 2, 8	crab 3145	. 2 class {𝑤 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}
10	1, 9	wceq 1536	1 wff TopVec = {𝑤 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}

This definition is referenced by:  istvc  22803