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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 2164 | . 2 | |
2 | 1 | toptopon 12563 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 2135 cuni 3783 cfv 5182 ctop 12542 TopOnctopon 12555 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-topon 12556 |
This theorem is referenced by: topontopon 12565 lmreltop 12740 cnovex 12743 cnptopco 12769 cnptopresti 12785 lmtopcnp 12797 lmcn 12798 txcnmpt 12820 txdis1cn 12825 lmcn2 12827 cnmpt1t 12832 cnmpt12 12834 cnmpt21 12838 cnmpt21f 12839 cnmpt2t 12840 cnmpt22 12841 cnmpt22f 12842 cnmptcom 12845 limccnp2lem 13192 limccnp2cntop 13193 |
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