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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsetindis | Unicode version |
Description: Axiom of bounded set induction using implicit substitutions. (Contributed by BJ, 22-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdsetindis.bd | BOUNDED |
bdsetindis.nf0 | |
bdsetindis.nf1 | |
bdsetindis.nf2 | |
bdsetindis.nf3 | |
bdsetindis.1 | |
bdsetindis.2 |
Ref | Expression |
---|---|
bdsetindis |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2178 | . . . . 5 | |
2 | bdsetindis.nf0 | . . . . 5 | |
3 | 1, 2 | nfralxy 2360 | . . . 4 |
4 | bdsetindis.nf1 | . . . 4 | |
5 | 3, 4 | nfim 1464 | . . 3 |
6 | nfcv 2178 | . . . . 5 | |
7 | bdsetindis.nf3 | . . . . 5 | |
8 | 6, 7 | nfralxy 2360 | . . . 4 |
9 | bdsetindis.nf2 | . . . 4 | |
10 | 8, 9 | nfim 1464 | . . 3 |
11 | raleq 2505 | . . . . 5 | |
12 | 11 | biimprd 147 | . . . 4 |
13 | bdsetindis.2 | . . . . 5 | |
14 | 13 | equcoms 1594 | . . . 4 |
15 | 12, 14 | imim12d 68 | . . 3 |
16 | 5, 10, 15 | cbv3 1630 | . 2 |
17 | bdsetindis.1 | . . . . . 6 | |
18 | 2, 17 | bj-sbime 9913 | . . . . 5 |
19 | 18 | ralimi 2384 | . . . 4 |
20 | 19 | imim1i 54 | . . 3 |
21 | 20 | alimi 1344 | . 2 |
22 | bdsetindis.bd | . . 3 BOUNDED | |
23 | 22 | ax-bdsetind 10093 | . 2 |
24 | 16, 21, 23 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wnf 1349 wsb 1645 wral 2306 BOUNDED wbd 9932 |
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 ax-bdsetind 10093 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 |
This theorem is referenced by: bj-inf2vnlem3 10097 |
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