d(x,y)={ 1 if x does not equal y

Question

0 if x=y

Prove that d satisfies the axioms of a metric.

clearly it satisfies d(x,y) existing in the reals, and d(x,y)>=0 and d(x,y)=0 iff x=y. why I don't know is triangle inequality and d(x,y)=d(y,x).