Set Difference is Right Distributive over Set Intersection

Theorem
Set difference is right distributive over set intersection.

Let $$R, S, T$$ be sets.

Then:
 * $$\left({R \cap S}\right) \setminus T = \left({R \setminus T}\right) \cap \left({S \setminus T}\right)$$

where:
 * $$R \cap S$$ denotes set intersection.
 * $$R \setminus T$$ denotes set difference;

Proof 1
Consider $$R, S, T \subseteq \mathbb U$$, where $$\mathbb U$$ is considered as the universe.

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Proof 2
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