
theorem
  for X being set holds X \ {} = X
proof
  let X be set;
  thus X \ {} c= X
  by XBOOLE_0:def 5;
  let x be object;
A1: not x in {} by XBOOLE_0:def 1;
  assume x in X;
  hence thesis by A1,XBOOLE_0:def 5;
end;
