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Theorem reusn 3869
 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.)
Assertion
Ref Expression
reusn
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reusn
StepHypRef Expression
1 euabsn2 3867 . 2
2 df-reu 2704 . 2
3 df-rab 2706 . . . 4
43eqeq1i 2442 . . 3
54exbii 1592 . 2
61, 2, 53bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  weu 2280  cab 2421  wreu 2699  crab 2701  csn 3806 This theorem is referenced by:  reusv6OLD  4726  reuen1  7168  cshwssizesame  28251  frisusgranb  28324  vdn1frgrav2  28353  vdgn1frgrav2  28354 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-reu 2704  df-rab 2706  df-sn 3812
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