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

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