Set Difference is Set

Theorem
Let $x$ be a small class.

Let $A$ be a class.

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

Then:


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

Proof
By Set Difference as Intersection with Relative Complement:


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

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

Therefore:


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