# Absorption Laws (Set Theory)/Union with Intersection/Proof 2

$S \cup \paren {S \cap T} = S$
 $\ds x$ $\in$ $\ds S \cup \paren {S \cap T}$ $\ds \leadstoandfrom \ \$ $\ds x$ $\in$ $\ds S \lor \paren {x \in S \land x \in T}$ Definition of Set Intersection and Definition of Set Union $\ds \leadstoandfrom \ \$ $\ds x$ $\in$ $\ds S$ Disjunction Absorbs Conjunction
$\blacksquare$