$\begin{align}  & \text{Let }a\in (X-Y)-Z \\ & a\in (X\cap Y')\cap Z' \\ & a\in X\text{ and }a\in Y'\text{ and }a\in Z' \\ & a\in X\text{ and }a\in Y'\text{ and }a\in X\text{ and }a\in Z' \\ & a\in X\cap Y'\text{ and }a\in X\cap Z' \\ & a\in (X\cap Y')\cap (X\cap Z') \\ & a\in (X-Y)\cap (X-Z) \\ & (X-Y)\cap (X-Z)\subseteq (X-Y)-Z----(i) \\ & \text{From the R}\text{.H}\text{.S} \\ & \text{Let }b\in (X-Y)\cap (X-Z) \\ & b\in (X\cap Y')\cap (X\cap Z') \\ & b\in (X\cap Y')\text{ and }b\in (X\cap Z') \\ & b\in X\text{ and }b\in Y'\text{ and }b\in X\text{ and }b\in Z' \\ & b\in X\text{ and }b\in Y'\text{ and }b\in Z' \\ & b\in (X\cap Y')\text{ and }b\in Z' \\ & b\in (X\cap Y')\cap Z' \\ & b\in (X-Y)-Z \\ & (X-Y)-Z\subseteq (X-Y)\cap (X-Z)---(ii) \\ & (X-Y)-Z=(X-Y)\cap (X-Z) \\\end{align}$