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

theorem Th41:
  for f being Function of X,Y st (Y = {} implies X = {}) & P c= X
  holds P c= f"(f.:P)
proof
  let f be Function of X,Y;
  assume Y <> {} or X = {};
  then dom f = X by Def1;
  hence thesis by FUNCT_1:76;
end;
