Set Difference is Anticommutative

Theorem
$$S - T = T - S \iff S = T$$

Proof
Suppose $$S = T$$.

Then $$S - T = \varnothing = T - S$$ from Set Difference Self Null.

Now suppose $$S - T = T - S$$. Then:

Similarly, $$T - S \subseteq S - T \Longrightarrow T \subseteq S$$.

Thus $$S \subseteq T$$ and $$T \subseteq S$$ and therefore $$S = T$$.