Complex sentence: For example, the axiom of separation was used to define the diagonal subset D, the axiom of extensionality was used to prove D\\ ne f (x), and the axiom of pairing was used in the definition of the subset P_1.
Split into simpler sentences: For example, the axiom of separation was used to define the diagonal subset D, and the axiom of extensionality was used to prove D\\ ne f (x). The axiom of pairing was used in the definition of the subset P_1.