Let f:R→R satisfy

f(a)≠0 for some a in R

f(xf(y))=yf(x) for all x,y in R
Prove that f(x)=f(x) for all x in R.
We only substitute x=0 and y=0, but that does not mean that variable y is dependent on variable x, right ? or it doesn't matter, I just want to be sure.
Thanks again