It is just a symmetry argument. Since if I have
A = {1, 3, 9}, B = {2, 5, 8}, C = {3, 4, 6, 7}
That is no different from:
A = {3, 4, 6, 7}, B = {2, 5, 8}, C = {1, 3, 9}
So we choose an arbitrary but consistent way to order them. That is A is always the set with the smallest minimum, C is always the set with the largest minimum. Then only the first ordering is valid and the other 5 are not checked.