Consider the following premises. For all z_2, z_2 is a doctor if and only if z_2 will write a letter. For all z_2, z_2 is a doctor. For all z_2, z_2 will make tea. Can we infer the following from them? If we can, name the inference rule being used: For all z_2, z_2 will write a letter.
 From the fact that for all z_2, z_2 is a doctor if and only if z_2 will write a letter we can infer that for all z_2, if z_2 were a doctor, then z_2 is writing a letter via universal biconditional elimination. From the fact that for all z_2, z_2 is a doctor, and that for all z_2, z_2 will make tea we can infer that for all z_2, z_2 is a doctor and z_2 will make tea via universal conjunction. From the fact that for all z_2, z_2 is a doctor and z_2 will make tea we can infer that for all z_2, z_2 is a doctor via universal simplification. Finally, from the fact that for all z_2, if z_2 were a doctor, then z_2 is writing a letter, and that for all z_2, z_2 is a doctor we can infer that for all z_2, z_2 will write a letter via universal modus ponens. Therefore, the answer is yes.