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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem2 | Unicode version |
Description: Lemma for bj-inf2vnlem3 14007 and bj-inf2vnlem4 14008. 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 2177 | . . . . . . 7 | |
2 | eqeq1 2177 | . . . . . . . 8 | |
3 | 2 | rexbidv 2471 | . . . . . . 7 |
4 | 1, 3 | orbi12d 788 | . . . . . 6 |
5 | 4 | rspcv 2830 | . . . . 5 |
6 | df-bj-ind 13962 | . . . . . . . . 9 Ind | |
7 | 6 | simplbi 272 | . . . . . . . 8 Ind |
8 | eleq1 2233 | . . . . . . . 8 | |
9 | 7, 8 | syl5ibr 155 | . . . . . . 7 Ind |
10 | 9 | a1dd 48 | . . . . . 6 Ind |
11 | vex 2733 | . . . . . . . . . 10 | |
12 | 11 | sucid 4402 | . . . . . . . . 9 |
13 | eleq2 2234 | . . . . . . . . . 10 | |
14 | 13 | eqcoms 2173 | . . . . . . . . 9 |
15 | 12, 14 | mpbii 147 | . . . . . . . 8 |
16 | eleq1 2233 | . . . . . . . . . . . . 13 | |
17 | eleq1 2233 | . . . . . . . . . . . . 13 | |
18 | 16, 17 | imbi12d 233 | . . . . . . . . . . . 12 |
19 | 18 | rspcv 2830 | . . . . . . . . . . 11 |
20 | bj-indsuc 13963 | . . . . . . . . . . . 12 Ind | |
21 | eleq1a 2242 | . . . . . . . . . . . 12 | |
22 | 20, 21 | syl6com 35 | . . . . . . . . . . 11 Ind |
23 | 19, 22 | syl8 71 | . . . . . . . . . 10 Ind |
24 | 23 | com13 80 | . . . . . . . . 9 Ind |
25 | 24 | com25 91 | . . . . . . . 8 Ind |
26 | 15, 25 | mpdi 43 | . . . . . . 7 Ind |
27 | 26 | rexlimiv 2581 | . . . . . 6 Ind |
28 | 10, 27 | jaoi 711 | . . . . 5 Ind |
29 | 5, 28 | syl6 33 | . . . 4 Ind |
30 | 29 | com3l 81 | . . 3 Ind |
31 | 30 | alrimdv 1869 | . 2 Ind |
32 | bi2.04 247 | . . 3 | |
33 | 32 | albii 1463 | . 2 |
34 | 31, 33 | syl6ib 160 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 703 wal 1346 wceq 1348 wcel 2141 wral 2448 wrex 2449 c0 3414 csuc 4350 Ind wind 13961 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-sn 3589 df-suc 4356 df-bj-ind 13962 |
This theorem is referenced by: bj-inf2vnlem3 14007 bj-inf2vnlem4 14008 |
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