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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 14729. 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 | biimpr 130 |
. . . . 5
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2 | jaob 710 |
. . . . . 6
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3 | 2 | biimpi 120 |
. . . . 5
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4 | simpl 109 |
. . . . . 6
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5 | eleq1 2240 |
. . . . . 6
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6 | 4, 5 | mpbidi 151 |
. . . . 5
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7 | 1, 3, 6 | 3syl 17 |
. . . 4
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8 | 7 | alimi 1455 |
. . 3
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9 | exim 1599 |
. . 3
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10 | 0ex 4131 |
. . . . . 6
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11 | 10 | isseti 2746 |
. . . . 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 14517 |
. . . 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 114 |
. . . . . 6
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18 | 1, 17 | syl 14 |
. . . . 5
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19 | 18 | alimi 1455 |
. . . 4
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20 | eqid 2177 |
. . . . 5
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21 | suceq 4403 |
. . . . . . 7
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22 | 21 | eqeq2d 2189 |
. . . . . 6
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23 | 22 | rspcev 2842 |
. . . . 5
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24 | 20, 23 | mpan2 425 |
. . . 4
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25 | vex 2741 |
. . . . . 6
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26 | 25 | bj-sucex 14678 |
. . . . 5
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27 | eqeq1 2184 |
. . . . . . 7
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28 | 27 | rexbidv 2478 |
. . . . . 6
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29 | eleq1 2240 |
. . . . . 6
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30 | 28, 29 | imbi12d 234 |
. . . . 5
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31 | 26, 30 | spcv 2832 |
. . . 4
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32 | 19, 24, 31 | syl2im 38 |
. . 3
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33 | 32 | ralrimiv 2549 |
. 2
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34 | df-bj-ind 14682 |
. 2
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35 | 16, 33, 34 | sylanbrc 417 |
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 4130 ax-pr 4210 ax-un 4434 ax-bd0 14568 ax-bdor 14571 ax-bdex 14574 ax-bdeq 14575 ax-bdel 14576 ax-bdsb 14577 ax-bdsep 14639 |
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-v 2740 df-dif 3132 df-un 3134 df-nul 3424 df-sn 3599 df-pr 3600 df-uni 3811 df-suc 4372 df-bdc 14596 df-bj-ind 14682 |
This theorem is referenced by: bj-inf2vn 14729 bj-inf2vn2 14730 |
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