Proving Metric Space Reflexivity with Three Conditions

[GridironCPJ]

Homework Statement

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)

Homework Equations

The three conditions above.

The Attempt at a Solution

I've gone in circles, getting nowhere.

 

[micromass]

I would start looking for a counterexample of what you're trying to prove.