Consider the following premises. For all z, if z were a doctor, then z is an electrician. For all z, if z were an electrician, then z is playing tennis. There is at least one z for which z is a doctor if and only if z will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is a doctor if and only if z will play tennis.
That is one of the premises. Therefore, the answer is yes.