In elementary robotics, it is very well known that the rotation of an object by the angles respectively Ψ (x), Θ (y), Φ (z) wrt** a fixed coordinate system (RPY) results in the same angular position for the object as the position achieved by the rotation of that object by the angles respectively Φ (z), Θ (y), Ψ (x) wrt a moving (with the object) coordinate system (euler angles). The proofs given up to now for such consequences are not general and for any such problem usually involve the calculation of the transformation matrix for both cases and observing the equivalence of the two matrices [1, 2, 3]. In this paper a fundamental and at the same time general proof is given for such results. It is shown that this equivalence in reverse order can be extended to the general class of transformations which keep the local relations constant (i.e., each transformation should keep the local relations constant). For example, rotation, translation and scaling are 3 types of transformations which can be located in this general class.