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Theorem snnzg 3756
Description: The singleton of a set is not empty. (Contributed by NM, 14-Dec-2008.)
Assertion
Ref Expression
snnzg  |-  ( A  e.  V  ->  { A }  =/=  (/) )

Proof of Theorem snnzg
StepHypRef Expression
1 snidg 3678 . 2  |-  ( A  e.  V  ->  A  e.  { A } )
2 ne0i 3474 . 2  |-  ( A  e.  { A }  ->  { A }  =/=  (/) )
31, 2syl 15 1  |-  ( A  e.  V  ->  { A }  =/=  (/) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696    =/= wne 2459   (/)c0 3468   {csn 3653
This theorem is referenced by:  snnz  3757  0nelop  4272  frirr  4386  frsn  4776  1stconst  6223  2ndconst  6224  pwsbas  13402  pwsle  13407  trnei  17603  uffix  17632  neiflim  17685  hausflim  17692  flimcf  17693  flimclslem  17695  cnpflf2  17711  cnpflf  17712  fclsfnflim  17738  dv11cn  19364  domrancur1b  25303  npmp  25624  conttnf2  25665  usgra1v  28260  elpaddat  30615  elpadd2at  30617
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-ne 2461  df-v 2803  df-dif 3168  df-nul 3469  df-sn 3659
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