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Theorem euabsn 3518
 Description: Another way to express existential uniqueness of a wff: its class abstraction is a singleton. (Contributed by NM, 22-Feb-2004.)
Assertion
Ref Expression
euabsn

Proof of Theorem euabsn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euabsn2 3517 . 2
2 nfv 1467 . . 3
3 nfab1 2231 . . . 4
43nfeq1 2239 . . 3
5 sneq 3463 . . . 4
65eqeq2d 2100 . . 3
72, 4, 6cbvex 1687 . 2
81, 7bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1290  wex 1427  weu 1949  cab 2075  csn 3452 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-eu 1952  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-sn 3458 This theorem is referenced by:  eusn  3522  args  4816  mapsn  6463
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