G is a group and $\displaystyle x,y\in G$.

Prove that $\displaystyle xy=yx$ iff $\displaystyle y^{-1}xy=x$ iff $\displaystyle x^{-1}y^{-1}xy=1$.

How can I break this statement up to prove. With iff proofs, I know we go both directions but how is it broken up when another iff is embedded in it?