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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 3190 |
. . 3
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3 | uniopn 13986 |
. . 3
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4 | 2, 3 | mpan2 425 |
. 2
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5 | 1, 4 | eqeltrid 2276 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4139 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-in 3150 df-ss 3157 df-pw 3595 df-uni 3828 df-top 13983 |
This theorem is referenced by: toponmax 14010 cldval 14084 ntrfval 14085 clsfval 14086 iscld 14088 ntrval 14095 clsval 14096 0cld 14097 ntrtop 14113 neifval 14125 neif 14126 neival 14128 isnei 14129 tpnei 14145 cnrest 14220 txcn 14260 |
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