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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem1 | Unicode version |
Description: Lemma for bj-inf2vn 13068. 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 129 | . . . . 5 | |
2 | jaob 684 | . . . . . 6 | |
3 | 2 | biimpi 119 | . . . . 5 |
4 | simpl 108 | . . . . . 6 | |
5 | eleq1 2180 | . . . . . 6 | |
6 | 4, 5 | mpbidi 150 | . . . . 5 |
7 | 1, 3, 6 | 3syl 17 | . . . 4 |
8 | 7 | alimi 1416 | . . 3 |
9 | exim 1563 | . . 3 | |
10 | 0ex 4025 | . . . . . 6 | |
11 | 10 | isseti 2668 | . . . . 5 |
12 | pm2.27 40 | . . . . 5 | |
13 | 11, 12 | ax-mp 5 | . . . 4 |
14 | bj-ex 12865 | . . . 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 1416 | . . . 4 |
20 | eqid 2117 | . . . . 5 | |
21 | suceq 4294 | . . . . . . 7 | |
22 | 21 | eqeq2d 2129 | . . . . . 6 |
23 | 22 | rspcev 2763 | . . . . 5 |
24 | 20, 23 | mpan2 421 | . . . 4 |
25 | vex 2663 | . . . . . 6 | |
26 | 25 | bj-sucex 13017 | . . . . 5 |
27 | eqeq1 2124 | . . . . . . 7 | |
28 | 27 | rexbidv 2415 | . . . . . 6 |
29 | eleq1 2180 | . . . . . 6 | |
30 | 28, 29 | imbi12d 233 | . . . . 5 |
31 | 26, 30 | spcv 2753 | . . . 4 |
32 | 19, 24, 31 | syl2im 38 | . . 3 |
33 | 32 | ralrimiv 2481 | . 2 |
34 | df-bj-ind 13021 | . 2 Ind | |
35 | 16, 33, 34 | sylanbrc 413 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 682 wal 1314 wceq 1316 wex 1453 wcel 1465 wral 2393 wrex 2394 c0 3333 csuc 4257 Ind wind 13020 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-nul 4024 ax-pr 4101 ax-un 4325 ax-bd0 12907 ax-bdor 12910 ax-bdex 12913 ax-bdeq 12914 ax-bdel 12915 ax-bdsb 12916 ax-bdsep 12978 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-nul 3334 df-sn 3503 df-pr 3504 df-uni 3707 df-suc 4263 df-bdc 12935 df-bj-ind 13021 |
This theorem is referenced by: bj-inf2vn 13068 bj-inf2vn2 13069 |
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