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Theorem euabsn2 3867
 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 2284 . 2
2 abeq1 2541 . . . 4
3 elsn 3821 . . . . . 6
43bibi2i 305 . . . . 5
54albii 1575 . . . 4
62, 5bitri 241 . . 3
76exbii 1592 . 2
81, 7bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549  wex 1550   wceq 1652   wcel 1725  weu 2280  cab 2421  csn 3806 This theorem is referenced by:  euabsn  3868  reusn  3869  absneu  3870  uniintab  4080  eusvobj2  6574 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-sn 3812
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