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Mirrors > Home > ILE Home > Th. List > rabss | Unicode version |
Description: Restricted class abstraction in a subclass relationship. (Contributed by NM, 16-Aug-2006.) |
Ref | Expression |
---|---|
rabss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2425 | . . 3 | |
2 | 1 | sseq1i 3123 | . 2 |
3 | abss 3166 | . 2 | |
4 | impexp 261 | . . . 4 | |
5 | 4 | albii 1446 | . . 3 |
6 | df-ral 2421 | . . 3 | |
7 | 5, 6 | bitr4i 186 | . 2 |
8 | 2, 3, 7 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wcel 1480 cab 2125 wral 2416 crab 2420 wss 3071 |
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 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rab 2425 df-in 3077 df-ss 3084 |
This theorem is referenced by: rabssdv 3177 dvdsssfz1 11550 phibndlem 11892 dfphi2 11896 istopon 12180 blsscls2 12662 |
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