The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for membranes as objects and anti-membranesas the corresponding annihilation counterpart in P systems. Natural numbers can berepresented by the corresponding number of membranes with a specific label. Computational completeness in this setting then can be obtained with using only elementarymembrane division rules, without using objects. A similar result can be obtained for tissue P systems with cell division rules and cell / anti-cell annihilation rules. In both cases,as derivation modes we may take the standard maximally parallel derivation modes aswell as any of the maximally parallel set derivation modes (non-extendable (multi)sets ofrules, (multi)sets with maximal number of rules, (multi)sets of rules affecting the maximalnumber of objects).