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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istopon 11962 |
. 2
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2 | 1 | simplbi 270 |
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-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-pr 4069 ax-un 4293 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-rab 2384 df-v 2643 df-sbc 2863 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-mpt 3931 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-iota 5024 df-fun 5061 df-fv 5067 df-topon 11960 |
This theorem is referenced by: topontopi 11965 topontopon 11969 toponmax 11974 topgele 11978 istps 11981 topontopn 11986 resttopon 12122 resttopon2 12129 lmfval 12143 cnfval 12145 cnpfval 12146 cnprcl2k 12156 cnpf2 12157 tgcn 12158 tgcnp 12159 iscnp4 12168 cnntr 12175 cncnp 12180 cnptopresti 12188 txtopon 12212 txcnp 12221 txlm 12229 cnmpt2res 12247 mopntop 12372 metcnpi 12439 metcnpi3 12441 dvfvalap 12523 dvfgg 12530 |
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