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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 3112 | . . 3 | |
3 | uniopn 12157 | . . 3 | |
4 | 2, 3 | mpan2 421 | . 2 |
5 | 1, 4 | eqeltrid 2224 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wss 3066 cuni 3731 ctop 12153 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-in 3072 df-ss 3079 df-pw 3507 df-uni 3732 df-top 12154 |
This theorem is referenced by: toponmax 12181 cldval 12257 ntrfval 12258 clsfval 12259 iscld 12261 ntrval 12268 clsval 12269 0cld 12270 ntrtop 12286 neifval 12298 neif 12299 neival 12301 isnei 12302 tpnei 12318 cnrest 12393 txcn 12433 |
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