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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 2142 | . . . . . . 7 | |
2 | 1 | ralbii 2330 | . . . . . 6 |
3 | df-ral 2311 | . . . . . 6 | |
4 | 2, 3 | bitri 173 | . . . . 5 |
5 | 4 | imbi1i 227 | . . . 4 |
6 | 5 | albii 1359 | . . 3 |
7 | ax-setind 4262 | . . 3 | |
8 | 6, 7 | sylbir 125 | . 2 |
9 | eqv 3240 | . 2 | |
10 | 8, 9 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wceq 1243 wcel 1393 wsb 1645 wral 2306 cvv 2557 |
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-setind 4262 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-v 2559 |
This theorem is referenced by: setind 4264 |
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