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Theorem absneu 3870
 Description: Restricted existential uniqueness determined by a singleton. (Contributed by NM, 29-May-2006.)
Assertion
Ref Expression
absneu

Proof of Theorem absneu
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3817 . . . . 5
21eqeq2d 2446 . . . 4
32spcegv 3029 . . 3
43imp 419 . 2
5 euabsn2 3867 . 2
64, 5sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wcel 1725  weu 2280  cab 2421  csn 3806 This theorem is referenced by:  rabsneu  3871 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sn 3812
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