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Mirrors > Home > ILE Home > Th. List > inex1 | Unicode version |
Description: Separation Scheme (Aussonderung) using class notation. Compare Exercise 4 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
inex1.1 |
Ref | Expression |
---|---|
inex1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inex1.1 | . . . 4 | |
2 | 1 | zfauscl 3898 | . . 3 |
3 | dfcleq 2075 | . . . . 5 | |
4 | elin 3155 | . . . . . . 7 | |
5 | 4 | bibi2i 225 | . . . . . 6 |
6 | 5 | albii 1399 | . . . . 5 |
7 | 3, 6 | bitri 182 | . . . 4 |
8 | 7 | exbii 1536 | . . 3 |
9 | 2, 8 | mpbir 144 | . 2 |
10 | 9 | issetri 2608 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 cvv 2601 cin 2972 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 |
This theorem is referenced by: inex2 3913 inex1g 3914 inuni 3930 bnd2 3947 peano5 4339 ssimaex 5255 ofmres 5783 tfrexlem 5971 |
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