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Theorem snnzg 3743
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 3665 . 2  |-  ( A  e.  V  ->  A  e.  { A } )
2 ne0i 3461 . 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 1684    =/= wne 2446   (/)c0 3455   {csn 3640
This theorem is referenced by:  snnz  3744  0nelop  4256  frirr  4370  frsn  4760  1stconst  6207  2ndconst  6208  pwsbas  13386  pwsle  13391  trnei  17587  uffix  17616  neiflim  17669  hausflim  17676  flimcf  17677  flimclslem  17679  cnpflf2  17695  cnpflf  17696  fclsfnflim  17722  dv11cn  19348  domrancur1b  25200  npmp  25521  conttnf2  25562  usgra1v  28126  elpaddat  29993  elpadd2at  29995
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-nul 3456  df-sn 3646
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