Set Difference with Set Difference/Proof 2

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Theorem

$S \setminus \paren {S \setminus T} = S \cap T = T \setminus \paren {T \setminus S}$


Proof

From the Axiom of Transitivity, all sets are classes.

The result then follows from Class Difference with Class Difference.


This needs considerable tedious hard slog to complete it.
In particular: Find the result that demonstrate the set difference of two sets is also a set, intersection as well. Probably via subset of set is set or something.
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Sources


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