m = n would be trivial and pointless. Also, I'm curious why he didn't specify precisely clarify "distinct" to mean "pairs of unequal values" (e.g., exclude {n,m} where n=m) and "pairs not equal to others" (e.g., {x,y} excludes {y,x}).
Adding "distinct" would have made it clearer, but it was obvious that the author meant distinct from reading the title alone.
It's math. No assumption is ever obvious. Only parts of some proofs are ever allowed to be called obvious.