Hi Bernhard,

The condition (x,y) = (x',y') is included for technical reasons, because the definition of an equivalence relation requires that a point must be equivalent to itself. If you look at the example here Equivalence relation - Wikipedia, the free encyclopedia you'll see that the equivalence relation contains each of the ordered pairs (a,a), (b,b) and (c,c). Let me know if anything is still confusing/unclear.

~GJA