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Theorem snnz 3882
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 3881 . 2  |-  ( A  e.  _V  ->  { A }  =/=  (/) )
31, 2ax-mp 8 1  |-  { A }  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1721    =/= wne 2567   _Vcvv 2916   (/)c0 3588   {csn 3774
This theorem is referenced by:  snsssn  3927  0nep0  4330  notzfaus  4334  nnullss  4385  opthwiener  4418  fparlem3  6407  fparlem4  6408  1n0  6698  fodomr  7217  mapdom3  7238  ssfii  7382  marypha1lem  7396  fseqdom  7863  dfac5lem3  7962  isfin1-3  8222  axcc2lem  8272  axdc4lem  8291  fpwwe2lem13  8473  isumltss  12583  0subg  14920  gsumxp  15505  lsssn0  15979  t1conperf  17452  isufil2  17893  cnextf  18050  ustuqtop1  18224  dveq0  19837  esumnul  24396  bdayfo  25543  nobndlem3  25562  filnetlem4  26300  diophrw  26707  dfac11  27028  bnj970  29024  dibn0  31636
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-v 2918  df-dif 3283  df-nul 3589  df-sn 3780
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