Union Absorbs Intersection/Proof 2

Theorem

$S \cup \paren {S \cap T} = S$

$\ds x$

$\in$

$\ds S \cup \paren {S \cap T}$

$\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 \ \ $

$\ds x$

$\in$

$\ds S$

$\blacksquare$