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Theorem snidg 3678
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 2296 . 2  |-  A  =  A
2 elsncg 3675 . 2  |-  ( A  e.  V  ->  ( A  e.  { A } 
<->  A  =  A ) )
31, 2mpbiri 224 1  |-  ( A  e.  V  ->  A  e.  { A } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    e. wcel 1696   {csn 3653
This theorem is referenced by:  snidb  3679  elsnc2g  3681  snnzg  3756  fvunsn  5728  fsnunf2  5735  fsnunfv  5736  1stconst  6223  2ndconst  6224  curry1  6226  curry2  6229  unifpw  7174  mapfien  7415  cfsuc  7899  eqs1  11463  swrds1  11489  rpnnen2lem9  12517  ramub1lem1  13089  ramub1lem2  13090  acsfiindd  14296  odf1o1  14899  gsumconst  15225  lspsolv  15912  maxlp  16894  cnpdis  17037  concompid  17173  dislly  17239  dfac14lem  17327  txtube  17350  pt1hmeo  17513  ufileu  17630  filufint  17631  uffix  17632  uffixsn  17636  i1fima2sn  19051  ply1rem  19565  esumel  23441  derangsn  23716  erdszelem4  23740  cvmlift2lem9  23857  vdgr1d  23909  vdgr1a  23912  eupap1  23915  cbicp  25269  fnckle  26148  lineval2a  26188  sgplpte21d1  26242  locfindis  26408  neibastop2lem  26412  ismrer1  26665  prtlem80  26827  kelac2  27266  rngunsnply  27481  en1uniel  27483  eldmressnsn  28089  funressnfv  28096  elpaddatriN  30614
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-sn 3659
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