https://maximummathematics.com/books/foundational-mathematics/set-theory/proof-technique-element-arguments/index.htmlIn the previous two sections, we provided proofs for two theorems (Theorem 3.4.1 and Theorem 3.3.1). Both proofs required that we select an arbitrary element from some set $A$, and show that because that arbitrarily chosen element satisfies some property, all elements of set $A$ satisfy that property. This is simply a rehash of the concept of Universal Specification and Universal Generalization as discussed in Chapter 2. In this section, we adapt the methods of Universal Specification and Universal Generalization to a new, powerful proof technique we can use for sets.Hugoen-US