reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem Th15:
  F1 is_transformable_to F2 implies for t1,t2 being transformation
  of F1,F2 st for a being Object of A holds t1.a = t2.a holds t1 = t2
proof
  assume
A1: F1 is_transformable_to F2;
  let t1,t2 be transformation of F1,F2;
  assume
A2: for a being Object of A holds t1.a = t2.a;
  now
    let a be Object of A;
    thus (t1 qua Function of the carrier of A, the carrier' of B).a = t1.a by
A1,Def4
      .= t2.a by A2
      .= (t2 qua Function of the carrier of A, the carrier' of B).a by A1,Def4;
  end;
  hence thesis;
end;
