Definition df-trg 21963

Description: Define a topological ring, which is a ring such that the addition is a topological group operation and the multiplication is continuous. (Contributed by Mario Carneiro, 5-Oct-2015.)

Assertion

Ref	Expression
df-trg	|- TopRing = { r e. ( TopGrp i^i Ring ) | (mulGrp ` r ) e. TopMnd }

Detailed syntax breakdown of Definition df-trg

Step	Hyp	Ref	Expression
1		ctrg 21959	. 2 class TopRing
2		vr	. . . . . 6 setvar r
3	2	cv 1482	. . . . 5 class r
4		cmgp 18489	. . . . 5 class mulGrp
5	3, 4	cfv 5888	. . . 4 class (mulGrp ` r )
6		ctmd 21874	. . . 4 class TopMnd
7	5, 6	wcel 1990	. . 3 wff (mulGrp ` r ) e. TopMnd
8		ctgp 21875	. . . 4 class TopGrp
9		crg 18547	. . . 4 class Ring
10	8, 9	cin 3573	. . 3 class ( TopGrp i^i Ring )
11	7, 2, 10	crab 2916	. 2 class { r e. ( TopGrp i^i Ring ) | (mulGrp ` r ) e. TopMnd }
12	1, 11	wceq 1483	1 wff TopRing = { r e. ( TopGrp i^i Ring ) | (mulGrp ` r ) e. TopMnd }

This definition is referenced by:  istrg  21967