reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem
  for x being object
  for f being Function of {x},Y st Y <> {} holds f.x in Y
proof let x be object;
  let f be Function of {x},Y;
  assume Y <> {};
  then
A1: dom f = {x} by Def1;
  rng f c= Y;
  then {f.x} c= Y by A1,FUNCT_1:4;
  hence thesis by ZFMISC_1:31;
end;
