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Mirrors > Home > ILE Home > Th. List > setindel | Unicode version |
Description: -Induction in terms of membership in a class. (Contributed by Mario Carneiro and Jim Kingdon, 22-Oct-2018.) |
Ref | Expression |
---|---|
setindel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clelsb3 2242 | . . . . . . 7 | |
2 | 1 | ralbii 2439 | . . . . . 6 |
3 | df-ral 2419 | . . . . . 6 | |
4 | 2, 3 | bitri 183 | . . . . 5 |
5 | 4 | imbi1i 237 | . . . 4 |
6 | 5 | albii 1446 | . . 3 |
7 | ax-setind 4447 | . . 3 | |
8 | 6, 7 | sylbir 134 | . 2 |
9 | eqv 3377 | . 2 | |
10 | 8, 9 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 wcel 1480 wsb 1735 wral 2414 cvv 2681 |
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 2119 ax-setind 4447 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-ral 2419 df-v 2683 |
This theorem is referenced by: setind 4449 |
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