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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 13560. 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 | biimpr 129 | . . . . 5 | |
2 | jaob 700 | . . . . . 6 | |
3 | 2 | biimpi 119 | . . . . 5 |
4 | simpl 108 | . . . . . 6 | |
5 | eleq1 2220 | . . . . . 6 | |
6 | 4, 5 | mpbidi 150 | . . . . 5 |
7 | 1, 3, 6 | 3syl 17 | . . . 4 |
8 | 7 | alimi 1435 | . . 3 |
9 | exim 1579 | . . 3 | |
10 | 0ex 4091 | . . . . . 6 | |
11 | 10 | isseti 2720 | . . . . 5 |
12 | pm2.27 40 | . . . . 5 | |
13 | 11, 12 | ax-mp 5 | . . . 4 |
14 | bj-ex 13347 | . . . 4 | |
15 | 13, 14 | syl 14 | . . 3 |
16 | 8, 9, 15 | 3syl 17 | . 2 |
17 | 3 | simprd 113 | . . . . . 6 |
18 | 1, 17 | syl 14 | . . . . 5 |
19 | 18 | alimi 1435 | . . . 4 |
20 | eqid 2157 | . . . . 5 | |
21 | suceq 4362 | . . . . . . 7 | |
22 | 21 | eqeq2d 2169 | . . . . . 6 |
23 | 22 | rspcev 2816 | . . . . 5 |
24 | 20, 23 | mpan2 422 | . . . 4 |
25 | vex 2715 | . . . . . 6 | |
26 | 25 | bj-sucex 13509 | . . . . 5 |
27 | eqeq1 2164 | . . . . . . 7 | |
28 | 27 | rexbidv 2458 | . . . . . 6 |
29 | eleq1 2220 | . . . . . 6 | |
30 | 28, 29 | imbi12d 233 | . . . . 5 |
31 | 26, 30 | spcv 2806 | . . . 4 |
32 | 19, 24, 31 | syl2im 38 | . . 3 |
33 | 32 | ralrimiv 2529 | . 2 |
34 | df-bj-ind 13513 | . 2 Ind | |
35 | 16, 33, 34 | sylanbrc 414 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 698 wal 1333 wceq 1335 wex 1472 wcel 2128 wral 2435 wrex 2436 c0 3394 csuc 4325 Ind wind 13512 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-nul 4090 ax-pr 4169 ax-un 4393 ax-bd0 13399 ax-bdor 13402 ax-bdex 13405 ax-bdeq 13406 ax-bdel 13407 ax-bdsb 13408 ax-bdsep 13470 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-nul 3395 df-sn 3566 df-pr 3567 df-uni 3773 df-suc 4331 df-bdc 13427 df-bj-ind 13513 |
This theorem is referenced by: bj-inf2vn 13560 bj-inf2vn2 13561 |
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