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Theorem rabsneu 3632
 Description: Restricted existential uniqueness determined by a singleton. (Contributed by NM, 29-May-2006.) (Revised by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
rabsneu

Proof of Theorem rabsneu
StepHypRef Expression
1 df-rab 2444 . . . 4
21eqeq1i 2165 . . 3
3 absneu 3631 . . 3
42, 3sylan2b 285 . 2
5 df-reu 2442 . 2
64, 5sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1335  weu 2006   wcel 2128  cab 2143  wreu 2437  crab 2439  csn 3560 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-reu 2442  df-rab 2444  df-v 2714  df-sn 3566 This theorem is referenced by: (None)
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