$\begin{align}  & (A\bigcap B\bigcap C)\bigcup (B\bigcap {A}')\bigcup (B\bigcap {C}')=B\bigcap ((A\bigcap C)\bigcup {A}'\bigcup {C}') \\  & =B\bigcap ((\underbrace{A\bigcap C)\bigcup (A\bigcap C{)}'}_{M})=B\xrightarrow{motammem}{B}' \\ \end{align}$