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Theorem snriota 6287
Description: A restricted class abstraction with a unique member can be expressed as a singleton. (Contributed by NM, 30-May-2006.)
Assertion
Ref Expression
snriota

Proof of Theorem snriota
StepHypRef Expression
1 df-reu 2814 . . 3
2 sniota 5583 . . 3
31, 2sylbi 195 . 2
4 df-rab 2816 . 2
5 df-riota 6257 . . 3
65sneqi 4040 . 2
73, 4, 63eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  {cab 2442  E!wreu 2809  {crab 2811  {csn 4029  iotacio 5554  iota_crio 6256
This theorem is referenced by:  divalgmod  14064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257
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