reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

theorem
  for E being non empty set, A being Event of E st A <> {} ex e being
  Singleton of E st e c= A
proof
  let E be non empty set, A be Event of E;
  set x = the Element of A;
  assume
A1: A <> {};
  then reconsider x as Element of E by TARSKI:def 3;
  {x} c= A by A1,ZFMISC_1:31;
  hence thesis;
end;
