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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 10769. Remark: unoptimized proof (have to use more deduction style). (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vnlem1 | Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2 128 | . . . . 5 | |
2 | jaob 663 | . . . . . 6 | |
3 | 2 | biimpi 118 | . . . . 5 |
4 | simpl 107 | . . . . . 6 | |
5 | eleq1 2141 | . . . . . 6 | |
6 | 4, 5 | mpbidi 149 | . . . . 5 |
7 | 1, 3, 6 | 3syl 17 | . . . 4 |
8 | 7 | alimi 1384 | . . 3 |
9 | exim 1530 | . . 3 | |
10 | 0ex 3905 | . . . . . 6 | |
11 | 10 | isseti 2607 | . . . . 5 |
12 | pm2.27 39 | . . . . 5 | |
13 | 11, 12 | ax-mp 7 | . . . 4 |
14 | bj-ex 10573 | . . . 4 | |
15 | 13, 14 | syl 14 | . . 3 |
16 | 8, 9, 15 | 3syl 17 | . 2 |
17 | 3 | simprd 112 | . . . . . 6 |
18 | 1, 17 | syl 14 | . . . . 5 |
19 | 18 | alimi 1384 | . . . 4 |
20 | eqid 2081 | . . . . 5 | |
21 | suceq 4157 | . . . . . . 7 | |
22 | 21 | eqeq2d 2092 | . . . . . 6 |
23 | 22 | rspcev 2701 | . . . . 5 |
24 | 20, 23 | mpan2 415 | . . . 4 |
25 | vex 2604 | . . . . . 6 | |
26 | 25 | bj-sucex 10714 | . . . . 5 |
27 | eqeq1 2087 | . . . . . . 7 | |
28 | 27 | rexbidv 2369 | . . . . . 6 |
29 | eleq1 2141 | . . . . . 6 | |
30 | 28, 29 | imbi12d 232 | . . . . 5 |
31 | 26, 30 | spcv 2691 | . . . 4 |
32 | 19, 24, 31 | syl2im 38 | . . 3 |
33 | 32 | ralrimiv 2433 | . 2 |
34 | df-bj-ind 10722 | . 2 Ind | |
35 | 16, 33, 34 | sylanbrc 408 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wo 661 wal 1282 wceq 1284 wex 1421 wcel 1433 wral 2348 wrex 2349 c0 3251 csuc 4120 Ind wind 10721 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-nul 3904 ax-pr 3964 ax-un 4188 ax-bd0 10604 ax-bdor 10607 ax-bdex 10610 ax-bdeq 10611 ax-bdel 10612 ax-bdsb 10613 ax-bdsep 10675 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-un 2977 df-nul 3252 df-sn 3404 df-pr 3405 df-uni 3602 df-suc 4126 df-bdc 10632 df-bj-ind 10722 |
This theorem is referenced by: bj-inf2vn 10769 bj-inf2vn2 10770 |
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