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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istopon 13404 |
. 2
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2 | 1 | simprbi 275 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-un 4433 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-iota 5178 df-fun 5218 df-fv 5224 df-topon 13402 |
This theorem is referenced by: toponunii 13408 toponmax 13416 toponss 13417 toponcom 13418 topgele 13420 topontopn 13428 restuni 13565 resttopon2 13571 lmfval 13585 cnfval 13587 cnpfval 13588 cnprcl2k 13599 ssidcn 13603 iscnp4 13611 cnntr 13618 cncnp 13623 cnptopresti 13631 txtopon 13655 txuni 13656 cnmpt1t 13678 cnmpt2t 13686 cnmpt1res 13689 cnmpt2res 13690 mopnuni 13838 isxms2 13845 limccnp2lem 14038 limccnp2cntop 14039 dvfvalap 14043 dvbss 14047 dvfgg 14050 dvcnp2cntop 14056 dvaddxxbr 14058 dvmulxxbr 14059 |
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