Consider the following premises. For all y_1, if y_1 were sad, then y_1 is an office clerk. There is at least one y_1 for which y_1 is sad if and only if y_1 is an office clerk. For all y_1, y_1 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which y_1 is not sad.
 From the fact that there is at least one y_1 for which y_1 is sad if and only if y_1 is an office clerk we can infer that there is at least one y_1 for which if y_1 were an office clerk, then y_1 is sad via existential biconditional elimination. From the fact that there is at least one y_1 for which if y_1 were an office clerk, then y_1 is sad, and that for all y_1, if y_1 were sad, then y_1 is an office clerk we can infer that there is at least one y_1 for which y_1 is an office clerk if and only if y_1 is sad via existential biconditional introduction. Finally, from the fact that there is at least one y_1 for which y_1 is an office clerk if and only if y_1 is sad, and that for all y_1, y_1 is not an office clerk we can infer that there is at least one y_1 for which y_1 is not sad via existential biconditional elimination. Therefore, the answer is yes.