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Mirrors > Home > ILE Home > Th. List > toptopon2 | Unicode version |
Description: A topology is the same thing as a topology on the union of its open sets. (Contributed by BJ, 27-Apr-2021.) |
Ref | Expression |
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toptopon2 |
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Step | Hyp | Ref | Expression |
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1 | eqid 2189 |
. 2
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2 | 1 | toptopon 13970 |
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 13963 |
This theorem is referenced by: topontopon 13972 lmreltop 14145 cnovex 14148 cnptopco 14174 cnptopresti 14190 lmtopcnp 14202 lmcn 14203 txcnmpt 14225 txdis1cn 14230 lmcn2 14232 cnmpt1t 14237 cnmpt12 14239 cnmpt21 14243 cnmpt21f 14244 cnmpt2t 14245 cnmpt22 14246 cnmpt22f 14247 cnmptcom 14250 limccnp2lem 14597 limccnp2cntop 14598 |
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