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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-om | Unicode version |
Description: A set is equal to ![]() |
Ref | Expression |
---|---|
bj-om |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omind 14568 |
. . . 4
![]() ![]() | |
2 | bj-indeq 14563 |
. . . 4
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3 | 1, 2 | mpbiri 168 |
. . 3
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4 | vex 2740 |
. . . . . 6
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5 | bj-omssind 14569 |
. . . . . 6
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6 | 4, 5 | ax-mp 5 |
. . . . 5
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7 | sseq1 3178 |
. . . . 5
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8 | 6, 7 | imbitrrid 156 |
. . . 4
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9 | 8 | alrimiv 1874 |
. . 3
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10 | 3, 9 | jca 306 |
. 2
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11 | bj-ssom 14570 |
. . . . . . 7
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12 | 11 | biimpi 120 |
. . . . . 6
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13 | 12 | adantl 277 |
. . . . 5
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14 | 13 | a1i 9 |
. . . 4
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15 | bj-omssind 14569 |
. . . . 5
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16 | 15 | adantrd 279 |
. . . 4
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17 | 14, 16 | jcad 307 |
. . 3
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18 | eqss 3170 |
. . 3
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19 | 17, 18 | syl6ibr 162 |
. 2
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20 | 10, 19 | impbid2 143 |
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-in1 614 ax-in2 615 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-13 2150 ax-14 2151 ax-ext 2159 ax-nul 4129 ax-pr 4209 ax-un 4433 ax-bd0 14447 ax-bdor 14450 ax-bdex 14453 ax-bdeq 14454 ax-bdel 14455 ax-bdsb 14456 ax-bdsep 14518 |
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-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-sn 3598 df-pr 3599 df-uni 3810 df-int 3845 df-suc 4371 df-iom 4590 df-bdc 14475 df-bj-ind 14561 |
This theorem is referenced by: bj-2inf 14572 bj-inf2vn 14608 bj-inf2vn2 14609 |
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