How to proof $A \times (B - C) \subseteq (A \times B) - (A \times C)$

Question

My attempt:

Suppose $x \in A \times (B - C).$ We know x is of the form $(a, d)$, where $a \in A$ and $d \in B - C$. We know, by the definition of -, that $d \in B$ and $d \notin C$.

Got stuck there and don't get how to synthetize a proof of the theorem

Answer 1

...where $a\in A$ and $d\in B-C$. We know by definition of $-$ that $d\in B$ and $d\notin C$.

That is to say, $~~~a\in A$ and $d\in B~~~$ as well as $~~~a\in A$ and $d\notin C$.

The first two imply that $(a,d)\in A\times B$ while the second two imply that $(a,d)\notin A\times C$

These together imply that...

$(a,d)\in (A\times B)-(A\times C)$ thus proving our desired claim.