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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | creg 20337 |
. 2
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2 | vy |
. . . . . . . 8
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3 | vz |
. . . . . . . 8
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4 | 2, 3 | wel 1890 |
. . . . . . 7
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5 | 3 | cv 1445 |
. . . . . . . . 9
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6 | vj |
. . . . . . . . . . 11
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7 | 6 | cv 1445 |
. . . . . . . . . 10
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8 | ccl 20045 |
. . . . . . . . . 10
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9 | 7, 8 | cfv 5585 |
. . . . . . . . 9
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10 | 5, 9 | cfv 5585 |
. . . . . . . 8
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11 | vx |
. . . . . . . . 9
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12 | 11 | cv 1445 |
. . . . . . . 8
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13 | 10, 12 | wss 3406 |
. . . . . . 7
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14 | 4, 13 | wa 371 |
. . . . . 6
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15 | 14, 3, 7 | wrex 2740 |
. . . . 5
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16 | 15, 2, 12 | wral 2739 |
. . . 4
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17 | 16, 11, 7 | wral 2739 |
. . 3
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18 | ctop 19929 |
. . 3
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19 | 17, 6, 18 | crab 2743 |
. 2
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20 | 1, 19 | wceq 1446 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: isreg 20360 |
Copyright terms: Public domain | W3C validator |