Set Difference is Set

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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

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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:

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

$\blacksquare$


Sources