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Theorem snec 7393
Description: The singleton of an equivalence class. (Contributed by NM, 29-Jan-1999.) (Revised by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
snec.1
Assertion
Ref Expression
snec

Proof of Theorem snec
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 snec.1 . . . 4
2 eceq1 7366 . . . . 5
32eqeq2d 2471 . . . 4
41, 3rexsn 4069 . . 3
54abbii 2591 . 2
6 df-qs 7336 . 2
7 df-sn 4030 . 2
85, 6, 73eqtr4ri 2497 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808   cvv 3109  {csn 4029  [cec 7328  /.cqs 7329
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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-ec 7332  df-qs 7336
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