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Theorem snm 3543
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 3541 . 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 1424    e. wcel 1436   _Vcvv 2615   {csn 3431
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-sn 3437
This theorem is referenced by:  mss  4027  ssfilem  6543  diffitest  6555  exmidfodomrlemim  6771
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