I have proved this using Venn diagram but when I am trying to prove this using the rule that "If $ A \subset B \text{ and } B \subset A $ then $ A = B $", I am having some problems with my understanding of the same,here is how I did so far:
Let $x \in A \cap (B-C) \Rightarrow x \in A \text{ and } x \in (B-C) \Rightarrow x \in A \text{ and } (x \in B \text{ and } x \notin C) $
How to proceed next? Since if I am do something like this: $ x \in A \text{ and } x \in B \text{ and } x \in A \text{ and } x \notin C $, it's not giving the correct results, what exactly I am missing here?