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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 4048 | . . 3 |
3 | dfcleq 2133 | . . . . 5 | |
4 | elin 3259 | . . . . . . 7 | |
5 | 4 | bibi2i 226 | . . . . . 6 |
6 | 5 | albii 1446 | . . . . 5 |
7 | 3, 6 | bitri 183 | . . . 4 |
8 | 7 | exbii 1584 | . . 3 |
9 | 2, 8 | mpbir 145 | . 2 |
10 | 9 | issetri 2695 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 cvv 2686 cin 3070 |
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 2121 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 |
This theorem is referenced by: inex2 4063 inex1g 4064 inuni 4080 bnd2 4097 peano5 4512 ssimaex 5482 ofmres 6034 tfrexlem 6231 elrest 12127 epttop 12259 tgrest 12338 resttopon 12340 restco 12343 cnrest2 12405 cnptopresti 12407 cnptoprest 12408 cnptoprest2 12409 txrest 12445 |
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