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Theorem euabsn2 3433
Description: Another way to express existential uniqueness of a wff: its class abstraction is a singleton. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
euabsn2  {  |  }  { }
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem euabsn2
StepHypRef Expression
1 df-eu 1903 . 2
2 abeq1 2147 . . . 4  {  |  }  { }  { }
3 elsn 3385 . . . . . 6  { }
43bibi2i 216 . . . . 5  { }
54albii 1359 . . . 4 
{ }
62, 5bitri 173 . . 3  {  |  }  { }
76exbii 1496 . 2  {  |  }  { }
81, 7bitr4i 176 1  {  |  }  { }
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1241   wceq 1243  wex 1381   wcel 1393  weu 1900   {cab 2026   {csn 3370
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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  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-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-sn 3376
This theorem is referenced by:  euabsn  3434  reusn  3435  absneu  3436  uniintabim  3646  euabex  3955  nfvres  5152  eusvobj2  5444
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