Let Y=f(X)+ \epsilon where  E[ \epsilon ] = 0

Let  EPE[x_0] = E_j[(y_0- \hat {f}(x_0))^2] , show that EPE[x_0]=Var(y_0|x_0)+(Bias( \hat {f}(x_0))^2+Var( \hat {f}(x_0)) where E_j is the expected value based upon training datas.

My proof so far.

I have  E_j[(y_0- \hat {f}(x_0)] = E_j[y_0- f(x_0)+f(x_0)-E_j[ \hat {f}(x_0)] + E_j[ \hat {f}(x_0)] - \hat {f}(x_0))^2]

But I'm having problem trying to write  Var (y_0|x_0) = E((y_0-E[y_0|x_0])^2|x_0] as terms that reassemble what I have up in there.

Thank you!