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 Th6:
  for f being Morphism of Functors(A,B) ex F1,F2 being Functor of A
,B, t being natural_transformation of F1,F2 st F1 is_naturally_transformable_to
  F2 & dom f = F1 & cod f = F2 & f = [[F1,F2],t]
proof
  let m be Morphism of Functors(A,B);
  Hom(dom m,cod m) <> {} & m is Morphism of dom m, cod m by CAT_1:2,4;
  then consider F,F1,t such that
A1: dom m = F & cod m = F1 and
A2: m = [[F,F1],t] by NATTRA_1:34;
  take F,F1,t;
  the carrier' of Functors(A,B) = NatTrans(A,B) by NATTRA_1:def 17;
  hence F is_naturally_transformable_to F1 by A2,NATTRA_1:32;
  thus thesis by A1,A2;
end;
