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Mirrors > Home > ILE Home > Th. List > ss2rab | Unicode version |
Description: Restricted abstraction classes in a subclass relationship. (Contributed by NM, 30-May-1999.) |
Ref | Expression |
---|---|
ss2rab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2426 | . . 3 | |
2 | df-rab 2426 | . . 3 | |
3 | 1, 2 | sseq12i 3130 | . 2 |
4 | ss2ab 3170 | . 2 | |
5 | df-ral 2422 | . . 3 | |
6 | imdistan 441 | . . . 4 | |
7 | 6 | albii 1447 | . . 3 |
8 | 5, 7 | bitr2i 184 | . 2 |
9 | 3, 4, 8 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1330 wcel 1481 cab 2126 wral 2417 crab 2421 wss 3076 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rab 2426 df-in 3082 df-ss 3089 |
This theorem is referenced by: ss2rabdv 3183 ss2rabi 3184 |
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