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Mirrors > Home > ILE Home > Th. List > rabxfrd | Unicode version |
Description: Class builder membership
after substituting an expression ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
rabxfrd.1 |
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rabxfrd.2 |
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rabxfrd.3 |
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rabxfrd.4 |
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rabxfrd.5 |
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Ref | Expression |
---|---|
rabxfrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabxfrd.3 |
. . . . . . . . . . 11
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2 | 1 | ex 115 |
. . . . . . . . . 10
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3 | ibibr 246 |
. . . . . . . . . 10
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4 | 2, 3 | sylib 122 |
. . . . . . . . 9
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5 | 4 | imp 124 |
. . . . . . . 8
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6 | 5 | anbi1d 465 |
. . . . . . 7
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7 | rabxfrd.4 |
. . . . . . . 8
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8 | 7 | elrab 2893 |
. . . . . . 7
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9 | rabid 2652 |
. . . . . . 7
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10 | 6, 8, 9 | 3bitr4g 223 |
. . . . . 6
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11 | 10 | rabbidva 2725 |
. . . . 5
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12 | 11 | eleq2d 2247 |
. . . 4
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13 | rabxfrd.1 |
. . . . 5
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14 | nfcv 2319 |
. . . . 5
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15 | rabxfrd.2 |
. . . . . 6
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16 | 15 | nfel1 2330 |
. . . . 5
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17 | rabxfrd.5 |
. . . . . 6
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18 | 17 | eleq1d 2246 |
. . . . 5
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19 | 13, 14, 16, 18 | elrabf 2891 |
. . . 4
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20 | nfrab1 2656 |
. . . . . 6
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21 | 13, 20 | nfel 2328 |
. . . . 5
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22 | eleq1 2240 |
. . . . 5
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23 | 13, 14, 21, 22 | elrabf 2891 |
. . . 4
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24 | 12, 19, 23 | 3bitr3g 222 |
. . 3
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25 | pm5.32 453 |
. . 3
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26 | 24, 25 | sylibr 134 |
. 2
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27 | 26 | imp 124 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rab 2464 df-v 2739 |
This theorem is referenced by: rabxfr 4470 |
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