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Mirrors > Home > ILE Home > Th. List > topontop | Unicode version |
Description: A topology on a given base set is a topology. (Contributed by Mario Carneiro, 13-Aug-2015.) |
Ref | Expression |
---|---|
topontop | TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istopon 12091 | . 2 TopOn | |
2 | 1 | simplbi 272 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cuni 3706 cfv 5093 ctop 12075 TopOnctopon 12088 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-topon 12089 |
This theorem is referenced by: topontopi 12094 topontopon 12098 toponmax 12103 topgele 12107 istps 12110 topontopn 12115 resttopon 12251 resttopon2 12258 lmfval 12272 cnfval 12274 cnpfval 12275 cnprcl2k 12286 cnpf2 12287 tgcn 12288 tgcnp 12289 iscnp4 12298 cnntr 12305 cncnp 12310 cnptopresti 12318 txtopon 12342 txcnp 12351 txlm 12359 cnmpt2res 12377 mopntop 12524 metcnpi 12595 metcnpi3 12597 dvfvalap 12730 dvfgg 12737 dvaddxxbr 12745 dvmulxxbr 12746 |
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