Set Difference is Set

Theorem
Let $x$ be a small class.

Let $A$ be a class.

Let $\mathscr M \left({ B }\right)$ denote that $B$ is small.

Then:


 * $\mathscr M \left({ x \setminus A }\right)$

Proof
By Set Difference as Intersection with Relative Complement, we know that:


 * $\left({ x \setminus A }\right) = \left({ x \cap \complement \left({ A }\right) }\right)$

Next, by Axiom of Subsets Equivalents, $\left({ x \cap \complement \left({ A }\right) }\right)$ is small.

Therefore:


 * $\mathscr M \left({ x \setminus A }\right)$