Consider the following premises. For all y, y is an office clerk if and only if y will go running. There is at least one y for which y is not an office clerk. For all y, if y were an office clerk, then y is running. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will go running.
 From the fact that for all y, y is an office clerk if and only if y will go running we can infer that for all y, if y goes running, then y is an office clerk via universal biconditional elimination. From the fact that for all y, if y goes running, then y is an office clerk, and that for all y, if y were an office clerk, then y is running we can infer that for all y, y will go running if and only if y is an office clerk via universal biconditional introduction. Finally, from the fact that for all y, y will go running if and only if y is an office clerk, and that there is at least one y for which y is not an office clerk we can infer that there is at least one y for which y will not go running via existential biconditional elimination, which contradicts that For all y, y will go running. Therefore, the answer is no.