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Theorem euabsn 3593
 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 3592 . 2
2 nfv 1508 . . 3
3 nfab1 2283 . . . 4
43nfeq1 2291 . . 3
5 sneq 3538 . . . 4
65eqeq2d 2151 . . 3
72, 4, 6cbvex 1729 . 2
81, 7bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331  wex 1468  weu 1999  cab 2125  csn 3527 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sn 3533 This theorem is referenced by:  eusn  3597  args  4908  mapsn  6584
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