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Mirrors > Home > ILE Home > Th. List > Mathboxes > setindis | Unicode version |
Description: Axiom of set induction using implicit substitutions. (Contributed by BJ, 22-Nov-2019.) |
Ref | Expression |
---|---|
setindis.nf0 | |
setindis.nf1 | |
setindis.nf2 | |
setindis.nf3 | |
setindis.1 | |
setindis.2 |
Ref | Expression |
---|---|
setindis |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2306 | . . . . 5 | |
2 | setindis.nf0 | . . . . 5 | |
3 | 1, 2 | nfralxy 2502 | . . . 4 |
4 | setindis.nf1 | . . . 4 | |
5 | 3, 4 | nfim 1559 | . . 3 |
6 | nfcv 2306 | . . . . 5 | |
7 | setindis.nf3 | . . . . 5 | |
8 | 6, 7 | nfralxy 2502 | . . . 4 |
9 | setindis.nf2 | . . . 4 | |
10 | 8, 9 | nfim 1559 | . . 3 |
11 | raleq 2659 | . . . . 5 | |
12 | 11 | biimprd 157 | . . . 4 |
13 | setindis.2 | . . . . 5 | |
14 | 13 | equcoms 1695 | . . . 4 |
15 | 12, 14 | imim12d 74 | . . 3 |
16 | 5, 10, 15 | cbv3 1729 | . 2 |
17 | setindis.1 | . . . . . 6 | |
18 | 2, 17 | bj-sbime 13495 | . . . . 5 |
19 | 18 | ralimi 2527 | . . . 4 |
20 | 19 | imim1i 60 | . . 3 |
21 | 20 | alimi 1442 | . 2 |
22 | ax-setind 4508 | . 2 | |
23 | 16, 21, 22 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wnf 1447 wsb 1749 wral 2442 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-setind 4508 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 |
This theorem is referenced by: bj-inf2vnlem4 13696 bj-findis 13702 |
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