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Mirrors > Home > MPE Home > Th. List > df-haus | Unicode version |
Description: Define the class of all Hausdorff spaces. A Hausdorff space is a topology in which distinct points have disjoint open neighborhoods. Definition of Hausdorff space in [Munkres] p. 98. (Contributed by NM, 8-Mar-2007.) |
Ref | Expression |
---|---|
df-haus |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cha 17326 |
. 2
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2 | vx |
. . . . . . . 8
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3 | 2 | cv 1648 |
. . . . . . 7
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4 | vy |
. . . . . . . 8
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5 | 4 | cv 1648 |
. . . . . . 7
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6 | 3, 5 | wne 2567 |
. . . . . 6
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7 | vn |
. . . . . . . . . 10
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8 | 2, 7 | wel 1722 |
. . . . . . . . 9
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9 | vm |
. . . . . . . . . 10
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10 | 4, 9 | wel 1722 |
. . . . . . . . 9
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11 | 7 | cv 1648 |
. . . . . . . . . . 11
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12 | 9 | cv 1648 |
. . . . . . . . . . 11
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13 | 11, 12 | cin 3279 |
. . . . . . . . . 10
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14 | c0 3588 |
. . . . . . . . . 10
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15 | 13, 14 | wceq 1649 |
. . . . . . . . 9
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16 | 8, 10, 15 | w3a 936 |
. . . . . . . 8
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17 | vj |
. . . . . . . . 9
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18 | 17 | cv 1648 |
. . . . . . . 8
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19 | 16, 9, 18 | wrex 2667 |
. . . . . . 7
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20 | 19, 7, 18 | wrex 2667 |
. . . . . 6
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21 | 6, 20 | wi 4 |
. . . . 5
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22 | 18 | cuni 3975 |
. . . . 5
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23 | 21, 4, 22 | wral 2666 |
. . . 4
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24 | 23, 2, 22 | wral 2666 |
. . 3
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25 | ctop 16913 |
. . 3
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26 | 24, 17, 25 | crab 2670 |
. 2
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27 | 1, 26 | wceq 1649 |
1
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Colors of variables: wff set class |
This definition is referenced by: ishaus 17340 |
Copyright terms: Public domain | W3C validator |