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Mirrors > Home > ILE Home > Th. List > isbasis2g | Unicode version |
Description: Express the predicate
"the set ![]() |
Ref | Expression |
---|---|
isbasis2g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isbasisg 14021 |
. 2
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2 | dfss3 3160 |
. . . 4
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3 | elin 3333 |
. . . . . . . . . 10
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4 | velpw 3597 |
. . . . . . . . . . 11
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5 | 4 | anbi2i 457 |
. . . . . . . . . 10
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6 | 3, 5 | bitri 184 |
. . . . . . . . 9
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7 | 6 | anbi2i 457 |
. . . . . . . 8
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8 | an12 561 |
. . . . . . . 8
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9 | 7, 8 | bitri 184 |
. . . . . . 7
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10 | 9 | exbii 1616 |
. . . . . 6
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11 | eluni 3827 |
. . . . . 6
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12 | df-rex 2474 |
. . . . . 6
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13 | 10, 11, 12 | 3bitr4i 212 |
. . . . 5
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14 | 13 | ralbii 2496 |
. . . 4
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15 | 2, 14 | bitri 184 |
. . 3
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16 | 15 | 2ralbii 2498 |
. 2
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17 | 1, 16 | bitrdi 196 |
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 |
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 3592 df-uni 3825 df-bases 14020 |
This theorem is referenced by: isbasis3g 14023 basis2 14025 fiinbas 14026 tgclb 14042 topbas 14044 restbasg 14145 txbas 14235 blbas 14410 |
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