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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 11993 |
. 2
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2 | dfss3 3037 |
. . . 4
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3 | elin 3206 |
. . . . . . . . . 10
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4 | selpw 3464 |
. . . . . . . . . . 11
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5 | 4 | anbi2i 448 |
. . . . . . . . . 10
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6 | 3, 5 | bitri 183 |
. . . . . . . . 9
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7 | 6 | anbi2i 448 |
. . . . . . . 8
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8 | an12 531 |
. . . . . . . 8
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9 | 7, 8 | bitri 183 |
. . . . . . 7
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10 | 9 | exbii 1552 |
. . . . . 6
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11 | eluni 3686 |
. . . . . 6
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12 | df-rex 2381 |
. . . . . 6
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13 | 10, 11, 12 | 3bitr4i 211 |
. . . . 5
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14 | 13 | ralbii 2400 |
. . . 4
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15 | 2, 14 | bitri 183 |
. . 3
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16 | 15 | 2ralbii 2402 |
. 2
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17 | 1, 16 | syl6bb 195 |
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 |
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-bases 11992 |
This theorem is referenced by: isbasis3g 11995 basis2 11997 fiinbas 11998 tgclb 12016 topbas 12018 restbasg 12119 txbas 12208 blbas 12361 |
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