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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 3067 |
. . 3
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3 | uniopn 11950 |
. . 3
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4 | 2, 3 | mpan2 419 |
. 2
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5 | 1, 4 | syl5eqel 2186 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-in 3027 df-ss 3034 df-pw 3459 df-uni 3684 df-top 11947 |
This theorem is referenced by: toponmax 11974 cldval 12050 ntrfval 12051 clsfval 12052 iscld 12054 ntrval 12061 clsval 12062 0cld 12063 ntrtop 12079 neifval 12091 neif 12092 neival 12094 isnei 12095 tpnei 12111 cnrest 12185 txcn 12225 |
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