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

theorem
  for A,B being set for f being Function st f in Funcs(A,B) holds dom f
  = A & rng f c= B
proof
  let A,B be set;
  let f be Function;
  assume f in Funcs(A,B);
  then ex g being Function st f = g & dom g = A & rng g c= B by Def2;
  hence thesis;
end;
