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

theorem
  for S being Functor of [:C,C9:],D, c being Object of C, c9 being
  Object of C9 holds (Obj S-?c9).c = (Obj S).(c,c9)
proof
  let S be Functor of [:C,C9:],D, c be Object of C, c9 be Object of C9;
  (S-?c9).(id c) = S.(id c,id c9) by FUNCT_5:70
    .= S.(id [c,c9]) by Th25
    .= id ((Obj S).[c,c9]) by CAT_1:68;
  hence thesis by CAT_1:67;
end;
