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Theorem euabsn2 3791
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 2208 . 2
2 abeq1 2459 . . . 4
3 elsn 3748 . . . . . 6
43bibi2i 304 . . . . 5
54albii 1566 . . . 4
62, 5bitri 240 . . 3
76exbii 1582 . 2
81, 7bitr4i 243 1
Colors of variables: wff setvar class
Syntax hints:   wb 176  wal 1540  wex 1541   wceq 1642   wcel 1710  weu 2204  cab 2339  csn 3737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-sn 3741
This theorem is referenced by:  euabsn  3792  reusn  3793  absneu  3794  uniintab  3964
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