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Theorem snnz 3757
Description: The singleton of a set is not empty. (Contributed by NM, 10-Apr-1994.)
Hypothesis
Ref Expression
snnz.1  |-  A  e. 
_V
Assertion
Ref Expression
snnz  |-  { A }  =/=  (/)

Proof of Theorem snnz
StepHypRef Expression
1 snnz.1 . 2  |-  A  e. 
_V
2 snnzg 3756 . 2  |-  ( A  e.  _V  ->  { A }  =/=  (/) )
31, 2ax-mp 8 1  |-  { A }  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1696    =/= wne 2459   _Vcvv 2801   (/)c0 3468   {csn 3653
This theorem is referenced by:  snsssn  3797  0nep0  4197  notzfaus  4201  nnullss  4251  opthwiener  4284  fparlem3  6236  fparlem4  6237  1n0  6510  fodomr  7028  mapdom3  7049  ssfii  7188  marypha1lem  7202  fseqdom  7669  dfac5lem3  7768  isfin1-3  8028  axcc2lem  8078  axdc4lem  8097  fpwwe2lem13  8280  isumltss  12323  0subg  14658  gsumxp  15243  lsssn0  15721  t1conperf  17178  isufil2  17619  dveq0  19363  esumnul  23442  bdayfo  24400  nobndlem3  24419  filnetlem4  26433  diophrw  26941  dfac11  27263  bnj970  29295  dibn0  31965
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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