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Mirrors > Home > MPE Home > Th. List > df-tdrg | Structured version Visualization version Unicode version |
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.) |
Ref | Expression |
---|---|
df-tdrg | TopDRing mulGrp ↾s Unit |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctdrg 21960 | . 2 TopDRing | |
2 | vr | . . . . . . 7 | |
3 | 2 | cv 1482 | . . . . . 6 |
4 | cmgp 18489 | . . . . . 6 mulGrp | |
5 | 3, 4 | cfv 5888 | . . . . 5 mulGrp |
6 | cui 18639 | . . . . . 6 Unit | |
7 | 3, 6 | cfv 5888 | . . . . 5 Unit |
8 | cress 15858 | . . . . 5 ↾s | |
9 | 5, 7, 8 | co 6650 | . . . 4 mulGrp ↾s Unit |
10 | ctgp 21875 | . . . 4 | |
11 | 9, 10 | wcel 1990 | . . 3 mulGrp ↾s Unit |
12 | ctrg 21959 | . . . 4 | |
13 | cdr 18747 | . . . 4 | |
14 | 12, 13 | cin 3573 | . . 3 |
15 | 11, 2, 14 | crab 2916 | . 2 mulGrp ↾s Unit |
16 | 1, 15 | wceq 1483 | 1 TopDRing mulGrp ↾s Unit |
Colors of variables: wff setvar class |
This definition is referenced by: istdrg 21969 |
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