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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem2 | Unicode version |
Description: Lemma for bj-inf2vnlem3 10097 and bj-inf2vnlem4 10098. Remark: unoptimized proof (have to use more deduction style). (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vnlem2 | Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2046 | . . . . . . 7 | |
2 | eqeq1 2046 | . . . . . . . 8 | |
3 | 2 | rexbidv 2327 | . . . . . . 7 |
4 | 1, 3 | orbi12d 707 | . . . . . 6 |
5 | 4 | rspcv 2652 | . . . . 5 |
6 | df-bj-ind 10051 | . . . . . . . . 9 Ind | |
7 | 6 | simplbi 259 | . . . . . . . 8 Ind |
8 | eleq1 2100 | . . . . . . . 8 | |
9 | 7, 8 | syl5ibr 145 | . . . . . . 7 Ind |
10 | 9 | a1dd 42 | . . . . . 6 Ind |
11 | vex 2560 | . . . . . . . . . 10 | |
12 | 11 | sucid 4154 | . . . . . . . . 9 |
13 | eleq2 2101 | . . . . . . . . . 10 | |
14 | 13 | eqcoms 2043 | . . . . . . . . 9 |
15 | 12, 14 | mpbii 136 | . . . . . . . 8 |
16 | eleq1 2100 | . . . . . . . . . . . . 13 | |
17 | eleq1 2100 | . . . . . . . . . . . . 13 | |
18 | 16, 17 | imbi12d 223 | . . . . . . . . . . . 12 |
19 | 18 | rspcv 2652 | . . . . . . . . . . 11 |
20 | bj-indsuc 10052 | . . . . . . . . . . . 12 Ind | |
21 | eleq1a 2109 | . . . . . . . . . . . 12 | |
22 | 20, 21 | syl6com 31 | . . . . . . . . . . 11 Ind |
23 | 19, 22 | syl8 65 | . . . . . . . . . 10 Ind |
24 | 23 | com13 74 | . . . . . . . . 9 Ind |
25 | 24 | com25 85 | . . . . . . . 8 Ind |
26 | 15, 25 | mpdi 38 | . . . . . . 7 Ind |
27 | 26 | rexlimiv 2427 | . . . . . 6 Ind |
28 | 10, 27 | jaoi 636 | . . . . 5 Ind |
29 | 5, 28 | syl6 29 | . . . 4 Ind |
30 | 29 | com3l 75 | . . 3 Ind |
31 | 30 | alrimdv 1756 | . 2 Ind |
32 | bi2.04 237 | . . 3 | |
33 | 32 | albii 1359 | . 2 |
34 | 31, 33 | syl6ib 150 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wo 629 wal 1241 wceq 1243 wcel 1393 wral 2306 wrex 2307 c0 3224 csuc 4102 Ind wind 10050 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-suc 4108 df-bj-ind 10051 |
This theorem is referenced by: bj-inf2vnlem3 10097 bj-inf2vnlem4 10098 |
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