New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  snec Unicode version

Theorem snec 5987
 Description: The singleton of an equivalence class. (Contributed by set.mm contributors, 29-Jan-1999.) (Revised by set.mm contributors, 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 5962 . . . . 5
32eqeq2d 2364 . . . 4
41, 3rexsn 3768 . . 3
54abbii 2465 . 2
6 df-qs 5951 . 2
7 df-sn 3741 . 2
85, 6, 73eqtr4ri 2384 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wcel 1710  cab 2339  wrex 2615  cvv 2859  csn 3737  cec 5945  cqs 5946 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861  df-sbc 3047  df-sn 3741  df-ima 4727  df-ec 5947  df-qs 5951 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator