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Theorem snm 3643
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 3641 . 2  |-  ( A  e.  _V  ->  E. x  x  e.  { A } )
31, 2ax-mp 5 1  |-  E. x  x  e.  { A }
Colors of variables: wff set class
Syntax hints:   E.wex 1468    e. wcel 1480   _Vcvv 2686   {csn 3527
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sn 3533
This theorem is referenced by:  mss  4148  ssfilem  6769  diffitest  6781  djuexb  6929  exmidonfinlem  7054  exmidfodomrlemim  7062  cc2lem  7086
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