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Theorem euabsn2 3624
 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 2006 . 2
2 abeq1 2264 . . . 4
3 velsn 3573 . . . . . 6
43bibi2i 226 . . . . 5
54albii 1447 . . . 4
62, 5bitri 183 . . 3
76exbii 1582 . 2
81, 7bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1330   wceq 1332  wex 1469  weu 2003   wcel 2125  cab 2140  csn 3556 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-sn 3562 This theorem is referenced by:  euabsn  3625  reusn  3626  absneu  3627  uniintabim  3840  euabex  4180  nfvres  5494  eusvobj2  5800
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