reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem Th30:
  for X being non empty set, f being Subset of X st f is Element
  of singletons(X) holds f is 1-element
proof
  let X be non empty set, f be Subset of X;
  assume f is Element of singletons(X);
  then f in singletons(X);
  then ex g being Subset of X st g = f & g is 1-element;
  hence thesis;
end;
