Not everyone is sure about replacement identity, the assumption that when a component of some artefact (or at least a very small component such as a brick) is replaced, the artefact remains the same. Some of these arguments are qualified by the assumption that the components are 'simple'. But what components are simple? An artefact like a bike is made from artefacts such as mudguards, wheels, brakes and so on. These artefacts (a brake e.g.) are built from other artefactual components such as rubber blocks, steel wingnuts, plastic cables and so on. An artefact such as a plastic cable is made of molecules. A molecule is not an artefact, of course, but it is complex, being made of atoms. An atom is made of sub-atomic particles and so on.
It seems entirely implausible that when a small sliver of material, or molecule or sub-atomic particle is shaved off the bike, the bike is no longer identical with the bike that existed before. So some qualified version of Replacement Identity must be true. But then the Transitivity of Identity kicks in. If the bike is the same bike after a tiny part has been removed and then replaced, then it is the same bike. And still the same bike after another part has been shaved off and replaced. And so on until the whole bike has been completely replaced. The enemies of (A) must bite the bullet. Either it is false, even for sub-atomic changes in composition. That seems implausible. Otherwise Replacement Identity + Transitivity gets us to the paradoxical conclusion. More on Transitivity later, as I promised.