
theorem Th1:
  for f being Function st f is nonpair-yielding holds rng f is without_pairs
proof
  let f be Function;
  assume
A1: for x being set st x in dom f holds f.x is non pair;
  let y be pair object;
  assume y in rng f;
  then ex x being object st x in dom f & y = f.x by FUNCT_1:def 3;
  hence thesis by A1;
end;
