Symmetric Difference is Associative/Proof 1

Proof
We can directly expand the expressions for $R \symdif \paren {S \symdif T}$ and $\paren {R \symdif S} \symdif T$, and see that they come to the same thing.

Expanding the :

Expanding the :

From Union is Commutative it is seen that the and  are the same, and the result is proved.