What was the idea of building up nuclear weapons that stopped each side from using them

Hello!

During the Cold War, the US and USSR competed in the build-up of nuclear weapons. What stopped both sides from using them was the fact that if one country attacked the other, the other country had the resources to attack in return. Neither country attacked the other because they knew that they would also be attacked. 

I hope this helps you! Have a great day!
-Mal