6.8.3 Set theory

Problem: Prove that: \[ \left(A_{1} \cap \ldots \cap A_{n}\right)-\left(B_{1} \cap \ldots \cap B_{n}\right) \subseteq\left(A_{1} \doteq B_{1}\right) \cup \ldots \cup\left(A_{n} \doteq B_{n}\right) \text {. } \]