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Mirrors > Home > ILE Home > Th. List > tgvalex | Unicode version |
Description: The topology generated by a basis is a set. (Contributed by Jim Kingdon, 4-Mar-2023.) |
Ref | Expression |
---|---|
tgvalex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgval 12733 |
. 2
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2 | inss1 3370 |
. . . . . . 7
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3 | 2 | unissi 3847 |
. . . . . 6
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4 | sstr 3178 |
. . . . . 6
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5 | 3, 4 | mpan2 425 |
. . . . 5
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6 | 5 | ss2abi 3242 |
. . . 4
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7 | df-pw 3592 |
. . . 4
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8 | 6, 7 | sseqtrri 3205 |
. . 3
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9 | uniexg 4454 |
. . . 4
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10 | 9 | pwexd 4196 |
. . 3
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11 | ssexg 4157 |
. . 3
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12 | 8, 10, 11 | sylancr 414 |
. 2
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13 | 1, 12 | eqeltrd 2266 |
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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-iota 5193 df-fun 5233 df-fv 5239 df-topgen 12731 |
This theorem is referenced by: ptex 12735 tgcl 13961 tgidm 13971 tgss3 13975 2basgeng 13979 tgrest 14066 txvalex 14151 txval 14152 txbasval 14164 |
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