It can be checked experimentaly. 3 travelers is traveling relative to each other. They send light with the same fraquency to each other and resieve the light with other fraquency. Then they can define their velocities and check the laws.
Energy factor has square power of velocity c, therefore delta energy can be variable in different frames. But velocity and gamma factor have unit power in formula of momentum. Because square root annihilate square power. Therefore delta momentum should be constant in any frame.