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 Th6:
  F is isomorphic implies for b being Object of B ex a being
  Object of A st F.a = b
proof
  assume
A1: F is isomorphic;
  let b be Object of B;
  rng Obj F = the carrier of B by A1;
  then consider a being object such that
A2: a in dom Obj F and
A3: (Obj F).a = b by FUNCT_1:def 3;
  reconsider a as Object of A by A2;
  take a;
  thus thesis by A3;
end;
