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Mirrors > Home > ILE Home > Th. List > toponuni | Unicode version |
Description: The base set of a topology on a given base set. (Contributed by Mario Carneiro, 13-Aug-2015.) |
Ref | Expression |
---|---|
toponuni | TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istopon 12180 | . 2 TopOn | |
2 | 1 | simprbi 273 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cuni 3736 cfv 5123 ctop 12164 TopOnctopon 12177 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-topon 12178 |
This theorem is referenced by: toponunii 12184 toponmax 12192 toponss 12193 toponcom 12194 topgele 12196 topontopn 12204 restuni 12341 resttopon2 12347 lmfval 12361 cnfval 12363 cnpfval 12364 cnprcl2k 12375 ssidcn 12379 iscnp4 12387 cnntr 12394 cncnp 12399 cnptopresti 12407 txtopon 12431 txuni 12432 cnmpt1t 12454 cnmpt2t 12462 cnmpt1res 12465 cnmpt2res 12466 mopnuni 12614 isxms2 12621 limccnp2lem 12814 limccnp2cntop 12815 dvfvalap 12819 dvbss 12823 dvfgg 12826 dvcnp2cntop 12832 dvaddxxbr 12834 dvmulxxbr 12835 |
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