Consider the following premises. For all x_13, x_13 is an office clerk if and only if x_13 will cook. There is at least one x_13 for which x_13 will cook or x_13 is a writer. For all x_13, if x_13 were a writer, then x_13 is an office clerk. For all x_13, x_13 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which x_13 is an office clerk and x_13 is a bartender.
 From the fact that for all x_13, x_13 is an office clerk if and only if x_13 will cook we can infer that for all x_13, if x_13 cooks, then x_13 is an office clerk via universal biconditional elimination. From the fact that for all x_13, if x_13 cooks, then x_13 is an office clerk, that for all x_13, if x_13 were a writer, then x_13 is an office clerk, and that there is at least one x_13 for which x_13 will cook or x_13 is a writer we can infer that there is at least one x_13 for which x_13 is an office clerk via existential disjunction elimination. Finally, from the fact that there is at least one x_13 for which x_13 is an office clerk, and that for all x_13, x_13 is a bartender we can infer that there is at least one x_13 for which x_13 is an office clerk and x_13 is a bartender via existential conjunction. Therefore, the answer is yes.