reserve A,B,C,D for Category,
  F for Functor of A,B,
  G for Functor of B,C;
reserve o,m for set;

theorem Th8:
  F is isomorphic implies F" is isomorphic
proof
  assume F is isomorphic;
  then
A1: F is one-to-one & F" = (F qua Function of the carrier' of A, the
  carrier' of B)" by Def2;
  hence F" is one-to-one by FUNCT_1:40;
  thus rng(F") = dom F by A1,FUNCT_1:33
    .= the carrier' of A by FUNCT_2:def 1;
end;
