Consider the following premises. For all x_7, x_7 is a nurse if and only if x_7 is an office clerk. There is at least one x_7 for which x_7 will write a letter. For all x_7, x_7 is a nurse. 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 x_7 will write a letter and x_7 is an office clerk.
 From the fact that for all x_7, x_7 is a nurse if and only if x_7 is an office clerk we can infer that for all x_7, if x_7 were a nurse, then x_7 is an office clerk via universal biconditional elimination. From the fact that for all x_7, if x_7 were a nurse, then x_7 is an office clerk, and that for all x_7, x_7 is a nurse we can infer that for all x_7, x_7 is an office clerk via universal modus ponens. Finally, from the fact that there is at least one x_7 for which x_7 will write a letter, and that for all x_7, x_7 is an office clerk we can infer that there is at least one x_7 for which x_7 will write a letter and x_7 is an office clerk via existential conjunction. Therefore, the answer is yes.