reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th18:
  for f being one-to-one Function holds card f = card rng f
proof
  let f be one-to-one Function;
A1: rng f = dom(f") & dom f = rng(f") by FUNCT_1:33;
  card rng f c= card dom f & card rng (f") c= card dom (f") by CARD_2:61;
  then card rng f = card dom f by A1;
  hence thesis by CARD_1:62;
end;
