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Theorem sniota 5583
Description: A class abstraction with a unique member can be expressed as a singleton. (Contributed by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
sniota

Proof of Theorem sniota
StepHypRef Expression
1 nfeu1 2294 . 2
2 nfab1 2621 . 2
3 nfiota1 5558 . . 3
43nfsn 4087 . 2
5 iota1 5570 . . . 4
6 eqcom 2466 . . . 4
75, 6syl6bb 261 . . 3
8 abid 2444 . . 3
9 vex 3112 . . . 4
109elsnc 4053 . . 3
117, 8, 103bitr4g 288 . 2
121, 2, 4, 11eqrd 3521 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  E!weu 2282  {cab 2442  {csn 4029  iotacio 5554
This theorem is referenced by:  snriota  6287
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-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
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