
theorem
  for S,T being non empty RelStr, f being Function of S,T st f is isomorphic
  holds f" is Function of T,S & rng (f") = the carrier of S
proof
  let S,T be non empty RelStr, f be Function of S,T;
  assume
A1: f is isomorphic;
  then
A2: rng f = the carrier of T by Th66;
A3: dom f = the carrier of S by FUNCT_2:def 1;
A4: dom (f") = the carrier of T by A1,A2,FUNCT_1:33;
  rng (f") = the carrier of S by A1,A3,FUNCT_1:33;
  hence thesis by A4,FUNCT_2:1;
end;
