Set Difference with Set Difference is Union of Set Difference with Intersection/Venn Diagram

Proof
Demonstration by Venn diagram:
 * Set-minus-set-diff-1.png Set-minus-set-diff-2.png

Consider the diagram on the.

The yellow area forms $S \setminus T$.

The red area forms $R \setminus \paren {S \setminus T}$.

Consider the diagram on the.

The yellow and orange areas together form $R \cap T$.

The red and orange areas together form $R \setminus S$.

The red, orange and yellow areas together form $\paren {R \setminus S} \cup \paren {R \cap T}$.

It is seen that the red area on the is the same as the red, orange and yellow areas together on the.