Is this proof of $(A \times B) - (A \times C) \subseteq A \times (B - C)$

Question

Suppose $x \in (A \times B) - (A \times C)$. We know $x \in (A \times B)$ and $x \notin (A \times C)$. We also know $x$ is a pair $(a, d)$, by the definition of $\times$, where $a \in A$ and $d \in B$ and $d \notin C$. Hence, $a \in A$ and $d \in B - C$. Hence $x \in A \times (B - C)$, which leads to $(A \times B) - (A \times C) \subseteq A \times (B - C)$ by the definition of subset.

Answer 1

Yes, your proof is correct. You have demonstrated every step of the proof very clearly.