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Theorem euabsn2 4034
 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 2323 . 2
2 abeq1 2581 . . . 4
3 elsn 3973 . . . . . 6
43bibi2i 320 . . . . 5
54albii 1699 . . . 4
62, 5bitri 257 . . 3
76exbii 1726 . 2
81, 7bitr4i 260 1
 Colors of variables: wff setvar class Syntax hints:   wb 189  wal 1450   wceq 1452  wex 1671   wcel 1904  weu 2319  cab 2457  csn 3959 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-sn 3960 This theorem is referenced by:  euabsn  4035  reusn  4036  absneu  4037  uniintab  4264  eusvobj2  6301
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