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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-inf2vnlem4 | Unicode version |
Description: Lemma for bj-inf2vn2 13173. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-inf2vnlem4 | Ind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-inf2vnlem2 13169 | . . 3 Ind | |
2 | nfv 1508 | . . . 4 | |
3 | nfv 1508 | . . . 4 | |
4 | nfv 1508 | . . . 4 | |
5 | nfv 1508 | . . . 4 | |
6 | eleq1 2202 | . . . . . 6 | |
7 | eleq1 2202 | . . . . . 6 | |
8 | 6, 7 | imbi12d 233 | . . . . 5 |
9 | 8 | biimpd 143 | . . . 4 |
10 | eleq1 2202 | . . . . . 6 | |
11 | eleq1 2202 | . . . . . 6 | |
12 | 10, 11 | imbi12d 233 | . . . . 5 |
13 | 12 | biimprd 157 | . . . 4 |
14 | 2, 3, 4, 5, 9, 13 | setindis 13165 | . . 3 |
15 | 1, 14 | syl6 33 | . 2 Ind |
16 | dfss2 3086 | . 2 | |
17 | 15, 16 | syl6ibr 161 | 1 Ind |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 697 wal 1329 wceq 1331 wcel 1480 wral 2416 wrex 2417 wss 3071 c0 3363 csuc 4287 Ind wind 13124 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-suc 4293 df-bj-ind 13125 |
This theorem is referenced by: bj-inf2vn2 13173 |
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