
theorem
  for C,C1,C2 being category, F1 being Functor of C1,C,
  F2 being Functor of C2,C st F1 is covariant & F2 is covariant holds
  [|F1,F2|] ~= [|F2,F1|]
  proof
    let C,C1,C2 be category;
    let F1 be Functor of C1,C;
    let F2 be Functor of C2,C;
    assume
A1: F1 is covariant & F2 is covariant;
A2: pr1(F1,F2) is covariant & pr2(F1,F2) is covariant &
    [|F1,F2|], pr1(F1,F2), pr2(F1,F2) is_pullback_of F1,F2 by A1,Th52;
A3: pr1(F2,F1) is covariant & pr2(F2,F1) is covariant &
    [|F2,F1|], pr1(F2,F1), pr2(F2,F1) is_pullback_of F2,F1 by A1,Th52;
    then [|F2,F1|], pr2(F2,F1), pr1(F2,F1) is_pullback_of F1,F2 by A1,Th47;
    hence [|F1,F2|] ~= [|F2,F1|] by A1,A2,A3,Th46;
  end;
