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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 12764 | . 2 TopOn | |
2 | 1 | simplbi 272 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 cuni 3794 cfv 5196 ctop 12748 TopOnctopon 12761 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-mpt 4050 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 df-topon 12762 |
This theorem is referenced by: topontopi 12767 topontopon 12771 toponmax 12776 topgele 12780 istps 12783 topontopn 12788 resttopon 12924 resttopon2 12931 lmfval 12945 cnfval 12947 cnpfval 12948 cnprcl2k 12959 cnpf2 12960 tgcn 12961 tgcnp 12962 iscnp4 12971 cnntr 12978 cncnp 12983 cnptopresti 12991 txtopon 13015 txcnp 13024 txlm 13032 cnmpt2res 13050 mopntop 13197 metcnpi 13268 metcnpi3 13270 dvfvalap 13403 dvfgg 13410 dvaddxxbr 13418 dvmulxxbr 13419 |
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