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Theorem sniota 5584
 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 2295 . 2
2 nfab1 2621 . 2
3 nfiota1 5559 . . 3
43nfsn 4089 . 2
5 iota1 5571 . . . 4
6 eqcom 2466 . . . 4
75, 6syl6bb 261 . . 3
8 abid 2444 . . 3
9 vex 3112 . . . 4
109elsnc 4056 . . 3
117, 8, 103bitr4g 288 . 2
121, 2, 4, 11eqrd 3517 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1395   wcel 1819  weu 2283  cab 2442  csn 4032  cio 5555 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  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 3476  df-in 3478  df-ss 3485  df-sn 4033  df-pr 4035  df-uni 4252  df-iota 5557 This theorem is referenced by:  snriota  6287
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