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Mirrors > Home > NFE 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 2208 | . 2 | |
2 | abeq1 2459 | . . . 4 | |
3 | elsn 3748 | . . . . . 6 | |
4 | 3 | bibi2i 304 | . . . . 5 |
5 | 4 | albii 1566 | . . . 4 |
6 | 2, 5 | bitri 240 | . . 3 |
7 | 6 | exbii 1582 | . 2 |
8 | 1, 7 | bitr4i 243 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wal 1540 wex 1541 wceq 1642 wcel 1710 weu 2204 cab 2339 csn 3737 |
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-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-sn 3741 |
This theorem is referenced by: euabsn 3792 reusn 3793 absneu 3794 uniintab 3964 |
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