$\begin{align*}
\overline{x}(\overline{y} + \overline{z}) + \overline{y} \cdot \overline{z} &= \overline{x}(\overline{yz}) + \overline{y+z} \\
&= \overline{x + yz} + \overline{y+z} \\
&= \overline{(x+yz) \cdot (y+z)} \\
&= \overline{xy+xz+yyz+yzz} \\
&= \overline{xy+xz+yz+yz} \\
&= \overline{xy+xz+yz} = \textrm{ ili} \\
&= \overline{xy} \cdot \overline{xz} \cdot \overline{yz} \\
&= (\overline{x} + \overline{y}) \cdot (\overline{x}+\overline{z}) \cdot (\overline{y}+\overline{z}) \\
&= \overline{x} \cdot \overline{y}+\overline{x} \cdot \overline{z}+\overline{y} \cdot \overline{z}
\end{align*}$