Consider the following premises. For all x_7, if x_7 were a doctor, then x_7 is a sailor. For all x_7, x_7 is a sailor if and only if x_7 will work. There is at least one x_7 for which if x_7 works, then x_7 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which if x_7 works, then x_7 is a sailor.
We can infer this via the existential transitivity rule. Therefore, the answer is yes.