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Theorem euabsn2 3479
 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 1946 . 2
2 abeq1 2192 . . . 4
3 velsn 3433 . . . . . 6
43bibi2i 225 . . . . 5
54albii 1400 . . . 4
62, 5bitri 182 . . 3
76exbii 1537 . 2
81, 7bitr4i 185 1
 Colors of variables: wff set class Syntax hints:   wb 103  wal 1283   wceq 1285  wex 1422   wcel 1434  weu 1943  cab 2069  csn 3416 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sn 3422 This theorem is referenced by:  euabsn  3480  reusn  3481  absneu  3482  uniintabim  3693  euabex  4008  nfvres  5258  eusvobj2  5549
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