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Theorem snm 3518
Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.)
Hypothesis
Ref Expression
snnz.1  |-  A  e. 
_V
Assertion
Ref Expression
snm  |-  E. x  x  e.  { A }
Distinct variable group:    x, A

Proof of Theorem snm
StepHypRef Expression
1 snnz.1 . 2  |-  A  e. 
_V
2 snmg 3516 . 2  |-  ( A  e.  _V  ->  E. x  x  e.  { A } )
31, 2ax-mp 7 1  |-  E. x  x  e.  { A }
Colors of variables: wff set class
Syntax hints:   E.wex 1422    e. wcel 1434   _Vcvv 2602   {csn 3406
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sn 3412
This theorem is referenced by:  mss  3989  ssfilem  6410  diffitest  6421
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