> 
> Let $d:X\times X\rightarrow \mathbb{R}$ such that:
> 
> 
> 1. $d(x,y)=0 \iff x=y$
> 2. $d(y,x)\leq d(z,y)+d(z,x)$
> 
> 
> 

I have started with symmetry:

Let $x=z$ so:
$$d(y,x)\leq d(x,y)+d(x,x)$$

$$d(y,x)\leq d(x,y)$$

But I can find how to prove $$d(y,x)\geq d(x,y)$$ to get an equality