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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 |
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Ref | Expression |
---|---|
topopn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1open.1 |
. 2
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2 | ssid 3175 |
. . 3
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3 | uniopn 13132 |
. . 3
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4 | 2, 3 | mpan2 425 |
. 2
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5 | 1, 4 | eqeltrid 2264 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4118 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-in 3135 df-ss 3142 df-pw 3576 df-uni 3808 df-top 13129 |
This theorem is referenced by: toponmax 13156 cldval 13232 ntrfval 13233 clsfval 13234 iscld 13236 ntrval 13243 clsval 13244 0cld 13245 ntrtop 13261 neifval 13273 neif 13274 neival 13276 isnei 13277 tpnei 13293 cnrest 13368 txcn 13408 |
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