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Theorem reusn 3432
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 3430 . 2  {  |  }  { }
2 df-reu 2307 . 2
3 df-rab 2309 . . . 4  {  |  }  {  |  }
43eqeq1i 2044 . . 3  {  |  }  { }  {  |  }  { }
54exbii 1493 . 2  {  |  }  { }  {  |  }  { }
61, 2, 53bitr4i 201 1  {  |  }  { }
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wceq 1242  wex 1378   wcel 1390  weu 1897   {cab 2023  wreu 2302   {crab 2304   {csn 3367
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-reu 2307  df-rab 2309  df-sn 3373
This theorem is referenced by:  reuen1  6217
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