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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 3877 | . . 3 |
3 | dfcleq 2034 | . . . . 5 | |
4 | elin 3126 | . . . . . . 7 | |
5 | 4 | bibi2i 216 | . . . . . 6 |
6 | 5 | albii 1359 | . . . . 5 |
7 | 3, 6 | bitri 173 | . . . 4 |
8 | 7 | exbii 1496 | . . 3 |
9 | 2, 8 | mpbir 134 | . 2 |
10 | 9 | issetri 2564 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 cin 2916 |
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-sep 3875 |
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-nfc 2167 df-v 2559 df-in 2924 |
This theorem is referenced by: inex2 3892 inex1g 3893 inuni 3909 bnd2 3926 peano5 4321 ssimaex 5234 ofmres 5763 tfrexlem 5948 |
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