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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 |
---|---|
toptopon2 | TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2117 | . 2 | |
2 | 1 | toptopon 12096 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1465 cuni 3706 cfv 5093 ctop 12075 TopOnctopon 12088 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-topon 12089 |
This theorem is referenced by: topontopon 12098 lmreltop 12273 cnovex 12276 cnptopco 12302 cnptopresti 12318 lmtopcnp 12330 lmcn 12331 txcnmpt 12353 txdis1cn 12358 lmcn2 12360 cnmpt1t 12365 cnmpt12 12367 cnmpt21 12371 cnmpt21f 12372 cnmpt2t 12373 cnmpt22 12374 cnmpt22f 12375 cnmptcom 12378 limccnp2lem 12725 limccnp2cntop 12726 |
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