theorem
  f is bijective & g=f" implies g is bijective
proof
  assume
A1: f is bijective & g=f";
  dom f = the carrier of X by FUNCT_2:def 1;
  then rng g = the carrier of X by A1,FUNCT_1:33;
  then
A2: g is onto by FUNCT_2:def 3;
  g is one-to-one by A1,FUNCT_1:40;
  hence thesis by A2;
end;
