Intersection Absorbs Union/Proof 2

Theorem

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

$\ds x$

$\in$

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

$\ds \leadstoandfrom \ \ $

$\ds x$

$\in$

$\ds S \land \paren {x \in S \lor x \in T}$

Definition of Set Intersection and Definition of Set Union

$\ds \leadstoandfrom \ \ $

$\ds x$

$\in$

$\ds S$

$\blacksquare$