I believe the principle you are referring to is deterrence. In nuclear strategy, deterrence refers to the ability of a state, in the case of nuclear attack, to launch a “second strike” against the attacking state, thus assuring that it will be equally destroyed. This idea of “mutually assured destruction” is therefore a major factor in preventing nuclear conflict and, while deterrence is less central in the post-Cold War world, is still a relevant principle. It should also be noted that the “nuclear club” is rather small, and that most member states have strong relationships (either as direct allies, such as the U.K. and France, or have extensive economic relationships, such as the U.S. and China).

In the post-Second World War period, interstate conflict (war between sovereign states) has decreased significantly, while intrastate conflict (conflict between differing groups within a state) has become the dominant form that conflict manifests. The changing nature of conflict is driven less by the existence of nuclear weapons, and due more to factors such as decolonization and the spreading of ideas of nationalism and ethnic identity/mobilization, increasing global interconnectivity due to globalization and advances in communication technology, the growth of international institutions which can mediate conflict, and the spreading of global norms (especially regarding the acceptance of the use of force). These have had a much more fundamental role in shaping the nature of conflict during the later half of the 20th century and presently.