reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem
  for T being Functor of C,D, T9 being Functor of C9,D9, c being Object
of C, c9 being Object of C9 holds (Obj [:T,T9:]).(c,c9) = [(Obj T).c,(Obj T9).
  c9]
proof
  let T be Functor of C,D, T9 be Functor of C9,D9;
  let c be Object of C, c9 be Object of C9;
A1: T.(id c) = id((Obj T).c) & T9.(id c9) = id((Obj T9).c9) by CAT_1:68;
A2: [id((Obj T).c),id((Obj T9).c9)] = id [(Obj T).c,(Obj T9).c9] by Th25;
  [:T,T9:].(id c,id c9) = [T.(id c),T9.(id c9)] & [id c,id c9] = id [c,c9]
  by Th25,FUNCT_3:75;
  hence thesis by A1,A2,CAT_1:67;
end;
