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Theorem snidg 3620
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 28-Oct-2003.)
Assertion
Ref Expression
snidg  |-  ( A  e.  V  ->  A  e.  { A } )

Proof of Theorem snidg
StepHypRef Expression
1 eqid 2177 . 2  |-  A  =  A
2 elsng 3606 . 2  |-  ( A  e.  V  ->  ( A  e.  { A } 
<->  A  =  A ) )
31, 2mpbiri 168 1  |-  ( A  e.  V  ->  A  e.  { A } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353    e. wcel 2148   {csn 3591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-sn 3597
This theorem is referenced by:  snidb  3621  elsn2g  3624  snnzg  3708  snmg  3709  exmidsssnc  4200  fvunsng  5705  fsnunfv  5712  1stconst  6215  2ndconst  6216  tfr0dm  6316  tfrlemibxssdm  6321  tfrlemi14d  6327  tfr1onlembxssdm  6337  tfr1onlemres  6343  tfrcllembxssdm  6350  tfrcllemres  6356  en1uniel  6797  onunsnss  6909  snon0  6928  supsnti  6997  fseq1p1m1  10067  elfzomin  10179  fsumsplitsnun  11398  divalgmod  11902  setsslid  12482  1strbas  12542  srnginvld  12570  lmodvscad  12584  mgm1  12668  mnd1id  12725  0subm  12748  cnpdis  13375  bj-sels  14288
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