I'm self-studying Introduction to Statistical Learning. Page 19 of the book states the following:

Consider a given estimate $\hat{f}$ and a set of predictors $X$, which yields the prediction $\hat{Y} = \hat{f}(X)$. Assume for a moment that both $\hat{f}$ and $X$ are fixed. Then, it is easy to show that

$$ E(Y-\hat{Y})^2 = E[f(X) + \epsilon - \hat{f}(X)]^2 = [f(X) = \hat{f}(X)]^2 + Var(\epsilon)$$

Question: How exactly is the step from $E[f(X) + \epsilon - \hat{f}(X)]^2$ to $[f(X) = \hat{f}(X)]^2 + Var(\epsilon)$ justified?



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