1. The problem statement, all variables and given/known data Show that the following three conditions of a metric space imply that d(x, y)=d(y, x): (1) d(x, y)>=0 for all x, y in R (2) d(x, y)=0 iff x=y (3) d(x, y)=<d(x, z)+d(z, y) for all x, y, z in R (Essentially, we can deduce a reduced-form definition of a metric space, one without explicitly stating the reflexivity condition because the other 3 conditions imply it) 2. Relevant equations The three conditions above. 3. The attempt at a solution I've gone in circles, getting nowhere.