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Mirrors > Home > ILE Home > Th. List > topnex | Unicode version |
Description: The class of all topologies is a proper class. The proof uses discrete topologies and pwnex 4308. (Contributed by BJ, 2-May-2021.) |
Ref | Expression |
---|---|
topnex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwnex 4308 |
. . . 4
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2 | 1 | neli 2364 |
. . 3
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3 | vex 2644 |
. . . . . . . 8
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4 | distop 12036 |
. . . . . . . 8
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5 | 3, 4 | ax-mp 7 |
. . . . . . 7
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6 | eleq1 2162 |
. . . . . . 7
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7 | 5, 6 | mpbiri 167 |
. . . . . 6
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8 | 7 | exlimiv 1545 |
. . . . 5
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9 | 8 | abssi 3119 |
. . . 4
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10 | ssexg 4007 |
. . . 4
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11 | 9, 10 | mpan 418 |
. . 3
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12 | 2, 11 | mto 629 |
. 2
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13 | 12 | nelir 2365 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-un 4293 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-nel 2363 df-ral 2380 df-rex 2381 df-v 2643 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-uni 3684 df-iun 3762 df-top 11947 |
This theorem is referenced by: (None) |
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