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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 14997. 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 711 |
. . . . . 6
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3 | 2 | biimpi 120 |
. . . . 5
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4 | simpl 109 |
. . . . . 6
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5 | eleq1 2250 |
. . . . . 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 1465 |
. . 3
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9 | exim 1609 |
. . 3
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10 | 0ex 4142 |
. . . . . 6
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11 | 10 | isseti 2757 |
. . . . 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 14785 |
. . . 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 1465 |
. . . 4
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20 | eqid 2187 |
. . . . 5
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21 | suceq 4414 |
. . . . . . 7
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22 | 21 | eqeq2d 2199 |
. . . . . 6
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23 | 22 | rspcev 2853 |
. . . . 5
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24 | 20, 23 | mpan2 425 |
. . . 4
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25 | vex 2752 |
. . . . . 6
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26 | 25 | bj-sucex 14946 |
. . . . 5
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27 | eqeq1 2194 |
. . . . . . 7
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28 | 27 | rexbidv 2488 |
. . . . . 6
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29 | eleq1 2250 |
. . . . . 6
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30 | 28, 29 | imbi12d 234 |
. . . . 5
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31 | 26, 30 | spcv 2843 |
. . . 4
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32 | 19, 24, 31 | syl2im 38 |
. . 3
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33 | 32 | ralrimiv 2559 |
. 2
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34 | df-bj-ind 14950 |
. 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 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-nul 4141 ax-pr 4221 ax-un 4445 ax-bd0 14836 ax-bdor 14839 ax-bdex 14842 ax-bdeq 14843 ax-bdel 14844 ax-bdsb 14845 ax-bdsep 14907 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-dif 3143 df-un 3145 df-nul 3435 df-sn 3610 df-pr 3611 df-uni 3822 df-suc 4383 df-bdc 14864 df-bj-ind 14950 |
This theorem is referenced by: bj-inf2vn 14997 bj-inf2vn2 14998 |
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