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Theorem sniota 5448
 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 2293 . . 3
2 iota1 5435 . . . . 5
3 eqcom 2440 . . . . 5
42, 3syl6bb 254 . . . 4
5 abid 2426 . . . 4
6 vex 2961 . . . . 5
76elsnc 3839 . . . 4
84, 5, 73bitr4g 281 . . 3
91, 8alrimi 1782 . 2
10 nfab1 2576 . . 3
11 nfiota1 5423 . . . 4
1211nfsn 3868 . . 3
1310, 12cleqf 2598 . 2
149, 13sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wceq 1653   wcel 1726  weu 2283  cab 2424  csn 3816  cio 5419 This theorem is referenced by:  snriota  6583 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-v 2960  df-sbc 3164  df-un 3327  df-sn 3822  df-pr 3823  df-uni 4018  df-iota 5421
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