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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 13973 |
. 2
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2 | 1 | simplbi 274 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-iota 5196 df-fun 5237 df-fv 5243 df-topon 13971 |
This theorem is referenced by: topontopi 13976 topontopon 13980 toponmax 13985 topgele 13989 istps 13992 topontopn 13997 resttopon 14131 resttopon2 14138 lmfval 14152 cnfval 14154 cnpfval 14155 cnprcl2k 14166 cnpf2 14167 tgcn 14168 tgcnp 14169 iscnp4 14178 cnntr 14185 cncnp 14190 cnptopresti 14198 txtopon 14222 txcnp 14231 txlm 14239 cnmpt2res 14257 mopntop 14404 metcnpi 14475 metcnpi3 14477 dvfvalap 14610 dvfgg 14617 dvaddxxbr 14625 dvmulxxbr 14626 |
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