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Theorem snm 3701
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 3699 . 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 1485    e. wcel 2141   _Vcvv 2730   {csn 3581
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-sn 3587
This theorem is referenced by:  mss  4209  ssfilem  6851  diffitest  6863  djuexb  7019  exmidonfinlem  7163  exmidfodomrlemim  7171  cc2lem  7221
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