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Mirrors > Home > ILE Home > Th. List > euabsn2 | Unicode version |
Description: Another way to express existential uniqueness of a wff: its class abstraction is a singleton. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
euabsn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2000 | . 2 | |
2 | abeq1 2247 | . . . 4 | |
3 | velsn 3539 | . . . . . 6 | |
4 | 3 | bibi2i 226 | . . . . 5 |
5 | 4 | albii 1446 | . . . 4 |
6 | 2, 5 | bitri 183 | . . 3 |
7 | 6 | exbii 1584 | . 2 |
8 | 1, 7 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 weu 1997 cab 2123 csn 3522 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sn 3528 |
This theorem is referenced by: euabsn 3588 reusn 3589 absneu 3590 uniintabim 3803 euabex 4142 nfvres 5447 eusvobj2 5753 |
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