TeX source:

\begin{split} \rho' &= \dfrac{\mathbf{A}_{\text{even}}\rho_{\text{EPR}}\mathbf{A}_{\text{even}}}{\langle00|\rho_{\text{EPR}}|00\rangle + \langle11|\rho_{\text{EPR}}|11\rangle} = \mathbf{A}_{\text{even}}\rho_{\text{EPR}}\mathbf{A}_{\text{even}} \\ &= (|00\rangle\langle00| + |11\rangle\langle11|)\dfrac{1}{2}(|00\rangle\langle00| + |11\rangle\langle11| + |00\rangle\langle11| + |11\rangle\langle00|)\mathbf{A}_{\text{even}} \\ &= \dfrac{1}{2}(|00\rangle\langle00| + |00\rangle\langle11| + |11\rangle\langle11| + |11\rangle\langle00|)\mathbf{A}_{\text{even}} \\ &= \dfrac{1}{2}(|00\rangle\langle00| + |00\rangle\langle11| + |11\rangle\langle11| + |11\rangle\langle00|)(|00\rangle\langle00| + |11\rangle\langle11|) \\ &= \dfrac{1}{2}(|00\rangle\langle00| + |00\rangle\langle11| + |11\rangle\langle11| + |11\rangle\langle00|) = \rho_{\text{EPR}}. \end{split}