What is equality? Are there different kinds of equality? Who is equal? And what are the consequences of treating others equally? This work investigates what kinds of equality can be applied to animals in a consistent way. It starts at the meta-ethical level, how to construct a coherent ethical system of universal ethical principles. Counteracting arbitrariness is of key importance at this level. Next it descends to the level of normative ethics, where counteracting inequality or discrimination becomes the central issue. Finally, it moves down to the level of applied ethics, with a focus on important problems in animal ethics, such as the predation problem. The end result will be a coherent ethical system with five basic principles. This ethical system generates five kinds of equality, solves the predation problem, proves that discrimination such as speciesism is based on a moral illusion and indicates that veganism is a moral duty that is consistent with our moral values.