Symmetric Difference is Associative

Theorem
Symmetric difference is associative:


 * $R \symdif \paren {S \symdif T} = \paren {R \symdif S} \symdif T$

Proof 2
There is another way of doing this.

Comment
This illustrates that you can express the symmetric difference of three sets as the union of four intersections (which seems more intuitively obvious) as well as the intersection of four unions (which is not quite so obvious).

Also see

 * Intersection is Associative
 * Union is Associative
 * Set Difference is not Associative