
theorem
  for C,D be set, f be total C-defined Function holds
  f is Function of C,D iff f is D-valued
  proof
    let C,D be set, f be total C-defined Function;
    reconsider f1 = f as Function of C, rng f by T2103;
    f1 is D-valued implies f is Function of dom f, D by N2103;
    hence thesis by PARTFUN1:def 2;
 end;
