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Mirrors > Home > MPE Home > Th. List > df-reg | Structured version Visualization version Unicode version |
Description: Define regular spaces. A space is regular if a point and a closed set can be separated by neighborhoods. (Contributed by Jeff Hankins, 1-Feb-2010.) |
Ref | Expression |
---|---|
df-reg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | creg 21113 | . 2 | |
2 | vy | . . . . . . . 8 | |
3 | vz | . . . . . . . 8 | |
4 | 2, 3 | wel 1991 | . . . . . . 7 |
5 | 3 | cv 1482 | . . . . . . . . 9 |
6 | vj | . . . . . . . . . . 11 | |
7 | 6 | cv 1482 | . . . . . . . . . 10 |
8 | ccl 20822 | . . . . . . . . . 10 | |
9 | 7, 8 | cfv 5888 | . . . . . . . . 9 |
10 | 5, 9 | cfv 5888 | . . . . . . . 8 |
11 | vx | . . . . . . . . 9 | |
12 | 11 | cv 1482 | . . . . . . . 8 |
13 | 10, 12 | wss 3574 | . . . . . . 7 |
14 | 4, 13 | wa 384 | . . . . . 6 |
15 | 14, 3, 7 | wrex 2913 | . . . . 5 |
16 | 15, 2, 12 | wral 2912 | . . . 4 |
17 | 16, 11, 7 | wral 2912 | . . 3 |
18 | ctop 20698 | . . 3 | |
19 | 17, 6, 18 | crab 2916 | . 2 |
20 | 1, 19 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: isreg 21136 |
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