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Definition df-tdrg 18191
 Description: Define a topological division ring (which differs from a topological field only in being potentially noncommutative), which is a division ring and topological ring such that the unit group of the division ring (which is the set of nonzero elements) is a topological group. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
df-tdrg TopDRing mulGrps Unit

Detailed syntax breakdown of Definition df-tdrg
StepHypRef Expression
1 ctdrg 18187 . 2 TopDRing
2 vr . . . . . . 7
32cv 1652 . . . . . 6
4 cmgp 15649 . . . . . 6 mulGrp
53, 4cfv 5455 . . . . 5 mulGrp
6 cui 15745 . . . . . 6 Unit
73, 6cfv 5455 . . . . 5 Unit
8 cress 13471 . . . . 5 s
95, 7, 8co 6082 . . . 4 mulGrps Unit
10 ctgp 18102 . . . 4
119, 10wcel 1726 . . 3 mulGrps Unit
12 ctrg 18186 . . . 4
13 cdr 15836 . . . 4
1412, 13cin 3320 . . 3
1511, 2, 14crab 2710 . 2 mulGrps Unit
161, 15wceq 1653 1 TopDRing mulGrps Unit
 Colors of variables: wff set class This definition is referenced by:  istdrg  18196
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