Set Difference Intersection with First Set is Set Difference/Proof 1

Theorem

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

Proof

\(\ds \paren {S \setminus T}\)

\(\subseteq\)

\(\ds S\)

Set Difference is Subset

\(\ds \leadsto \ \ \)

\(\ds \paren {S \setminus T} \cap S\)

\(=\)

\(\ds S \setminus T\)

Intersection with Subset is Subset‎

$\blacksquare$