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Theorem snriota 6582
 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-rab 2716 . . 3
2 df-reu 2714 . . . 4
3 sniota 5447 . . . 4
42, 3sylbi 189 . . 3
51, 4syl5eq 2482 . 2
6 riotaiota 6557 . . 3
76sneqd 3829 . 2
85, 7eqtr4d 2473 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  weu 2283  cab 2424  wreu 2709  crab 2711  csn 3816  cio 5418  crio 6544 This theorem is referenced by:  divalgmod  12928 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-un 3327  df-if 3742  df-sn 3822  df-pr 3823  df-uni 4018  df-iota 5420  df-riota 6551
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