We are given that \[ A \subset B. \]
We are required to show that \[ C - B \subset C - A. \]
Let \[ x \in C - B. \]
Then by definition of set difference,
\[ x \in C \quad \text{and} \quad x \notin B. \]
Since \[ A \subset B, \] every element of \( A \) is also an element of \( B \).
Hence, if \[ x \notin B, \] then \[ x \notin A. \]
Therefore, we have
\[ x \in C \quad \text{and} \quad x \notin A. \]
This implies
\[ x \in C - A. \]
Hence,
\[ C - B \subset C - A. \]
Thus, it is proved that if \[ A \subset B, \] then \[ C - B \subset C - A. \]