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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 13343. Remark: unoptimized proof (have to use more deduction style). (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vnlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2 129 |
. . . . 5
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2 | jaob 700 |
. . . . . 6
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3 | 2 | biimpi 119 |
. . . . 5
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4 | simpl 108 |
. . . . . 6
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5 | eleq1 2203 |
. . . . . 6
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6 | 4, 5 | mpbidi 150 |
. . . . 5
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7 | 1, 3, 6 | 3syl 17 |
. . . 4
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8 | 7 | alimi 1432 |
. . 3
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9 | exim 1579 |
. . 3
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10 | 0ex 4063 |
. . . . . 6
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11 | 10 | isseti 2697 |
. . . . 5
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12 | pm2.27 40 |
. . . . 5
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13 | 11, 12 | ax-mp 5 |
. . . 4
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14 | bj-ex 13140 |
. . . 4
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15 | 13, 14 | syl 14 |
. . 3
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16 | 8, 9, 15 | 3syl 17 |
. 2
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17 | 3 | simprd 113 |
. . . . . 6
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18 | 1, 17 | syl 14 |
. . . . 5
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19 | 18 | alimi 1432 |
. . . 4
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20 | eqid 2140 |
. . . . 5
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21 | suceq 4332 |
. . . . . . 7
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22 | 21 | eqeq2d 2152 |
. . . . . 6
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23 | 22 | rspcev 2793 |
. . . . 5
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24 | 20, 23 | mpan2 422 |
. . . 4
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25 | vex 2692 |
. . . . . 6
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26 | 25 | bj-sucex 13292 |
. . . . 5
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27 | eqeq1 2147 |
. . . . . . 7
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28 | 27 | rexbidv 2439 |
. . . . . 6
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29 | eleq1 2203 |
. . . . . 6
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30 | 28, 29 | imbi12d 233 |
. . . . 5
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31 | 26, 30 | spcv 2783 |
. . . 4
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32 | 19, 24, 31 | syl2im 38 |
. . 3
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33 | 32 | ralrimiv 2507 |
. 2
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34 | df-bj-ind 13296 |
. 2
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35 | 16, 33, 34 | sylanbrc 414 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-nul 4062 ax-pr 4139 ax-un 4363 ax-bd0 13182 ax-bdor 13185 ax-bdex 13188 ax-bdeq 13189 ax-bdel 13190 ax-bdsb 13191 ax-bdsep 13253 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-dif 3078 df-un 3080 df-nul 3369 df-sn 3538 df-pr 3539 df-uni 3745 df-suc 4301 df-bdc 13210 df-bj-ind 13296 |
This theorem is referenced by: bj-inf2vn 13343 bj-inf2vn2 13344 |
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