reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th19:
  for F being Functor of [:A,B:],C, a being Object of A holds (
  export F).a is Functor of B,C
proof
  let F be Functor of [:A,B:],C, a be Object of A;
  (export F).a = (F?-a) by Th18;
  hence thesis;
end;
