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

theorem Th11:
  for f being Function of X,Y st y in rng f
    ex x being object st x in X & f.x = y
proof
  let f be Function of X,Y;
  assume
A1: y in rng f;
  then dom f = X by Def1;
  hence thesis by A1,FUNCT_1:def 3;
end;
