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Mirrors > Home > ILE Home > Th. List > topopn | Unicode version |
Description: The underlying set of a topology is an open set. (Contributed by NM, 17-Jul-2006.) |
Ref | Expression |
---|---|
1open.1 |
Ref | Expression |
---|---|
topopn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1open.1 | . 2 | |
2 | ssid 3157 | . . 3 | |
3 | uniopn 12546 | . . 3 | |
4 | 2, 3 | mpan2 422 | . 2 |
5 | 1, 4 | eqeltrid 2251 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 wss 3111 cuni 3783 ctop 12542 |
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-ext 2146 ax-sep 4094 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-pw 3555 df-uni 3784 df-top 12543 |
This theorem is referenced by: toponmax 12570 cldval 12646 ntrfval 12647 clsfval 12648 iscld 12650 ntrval 12657 clsval 12658 0cld 12659 ntrtop 12675 neifval 12687 neif 12688 neival 12690 isnei 12691 tpnei 12707 cnrest 12782 txcn 12822 |
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