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Mirrors > Home > ILE Home > Th. List > reusn | Unicode version |
Description: A way to express restricted existential uniqueness of a wff: its restricted class abstraction is a singleton. (Contributed by NM, 30-May-2006.) (Proof shortened by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
reusn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euabsn2 3439 | . 2 | |
2 | df-reu 2313 | . 2 | |
3 | df-rab 2315 | . . . 4 | |
4 | 3 | eqeq1i 2047 | . . 3 |
5 | 4 | exbii 1496 | . 2 |
6 | 1, 2, 5 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 weu 1900 cab 2026 wreu 2308 crab 2310 csn 3375 |
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 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-reu 2313 df-rab 2315 df-v 2559 df-sn 3381 |
This theorem is referenced by: reuen1 6281 |
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