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Mirrors > Home > NFE 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 2623 | . . 3 | |
2 | df-rab 2623 | . . 3 | |
3 | 1, 2 | sseq12i 3297 | . 2 |
4 | ss2ab 3334 | . 2 | |
5 | df-ral 2619 | . . 3 | |
6 | imdistan 670 | . . . 4 | |
7 | 6 | albii 1566 | . . 3 |
8 | 5, 7 | bitr2i 241 | . 2 |
9 | 3, 4, 8 | 3bitri 262 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wal 1540 wcel 1710 cab 2339 wral 2614 crab 2618 wss 3257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rab 2623 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 |
This theorem is referenced by: ss2rabdv 3347 ss2rabi 3348 |
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