Consider the following premises. If Joseph cooks, then Susan is a doctor. Joseph is cooking if and only if David is poor. If Susan were a doctor, then Joseph is cooking. Can we infer the following from them? If we can, name the inference rule being used: If Susan were a doctor, then David is poor.
 From the fact that if Susan were a doctor, then Joseph is cooking, and that if Joseph cooks, then Susan is a doctor we can infer that Susan is a doctor if and only if Joseph is cooking via biconditional introduction. From the fact that Joseph is cooking if and only if David is poor we can infer that if Joseph cooks, then David is poor via biconditional elimination. From the fact that Susan is a doctor if and only if Joseph is cooking we can infer that if Susan were a doctor, then Joseph is cooking via biconditional elimination. Finally, from the fact that if Susan were a doctor, then Joseph is cooking, and that if Joseph cooks, then David is poor we can infer that if Susan were a doctor, then David is poor via transitivity. Therefore, the answer is yes.