Set Difference is Set

Theorem
Let $x$ be a small class.

Let $A$ be a class.

Let $\map \MM B$ denote that $B$ is small.

Then:


 * $\map \MM {x \setminus A}$

Proof
By Set Difference as Intersection with Relative Complement:


 * $\paren {x \setminus A} = \paren {x \cap \map \complement A}$

Next, by Axiom of Subsets Equivalents, $\paren {x \cap \map \complement A}$ is small.

Therefore:


 * $\map \MM {x \setminus A}$