Game theory:Baye's rule for tournament

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I'm having challenge with the following computations from the book I'm using. How are the steps obtain from the preceding step?

In the expressions below, $E_i$ and $E_j$ are independent, random variables with zero mean (error terms) while $e_i$ and $e_j$ are constants, $f$ and $F$ are pdfs and cdfs.

\begin{align*}&\Pr[E_i> e_j+ E_j- e_i]= \int_{-\infty}^{+\infty} \Pr[\left. E_i> e_j+ E_j- e_i \right|E_j]\cdot f_j(E_j)\,dE_j = \\ &=\int_{-\infty}^{+\infty}[1-F_i(e_j+ E_j- e_i )] \,f_j(E_j )dE_j \end{align*}