Exact law of mortality dynamics in changing populations and environment is derived. The law is universal for all species, from single cell yeast to humans. It includes no characteristics of animal- environment interactions (metabolism etc) which are a must for life. Such law is unique for live systems with their homeostatic self-adjustment to environment. Its universal dynamics for all animals, with their drastically different biology, evolutionary history, and complexity, is also unique for live systems-cf different thermodynamics of e.g. liquids and glasses. The law which is valid for all live, and only live, systems is a life specific law of nature. Mortality is an instrument of natural selection and biological diversity. Its law which is preserved in evolution of all species is a conservation law of mortality, selection, evolution, biology. The law implies new kind of mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species specific natural selection, proceed via universal stepwise rungs. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence.