Consider the following premises. For all x_13, x_13 is an office clerk. There is at least one x_13 for which x_13 is an office clerk if and only if x_13 will go running. 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 will go running or x_13 is an astronaut.
 From the fact that there is at least one x_13 for which x_13 is an office clerk if and only if x_13 will go running we can infer that there is at least one x_13 for which if x_13 were an office clerk, then x_13 is running via existential biconditional elimination. From the fact that there is at least one x_13 for which if x_13 were an office clerk, then x_13 is running, and that for all x_13, x_13 is an office clerk we can infer that there is at least one x_13 for which x_13 will go running via existential modus ponens. Finally, from the fact that there is at least one x_13 for which x_13 will go running we can infer that there is at least one x_13 for which x_13 will go running or x_13 is an astronaut via existential addition. Therefore, the answer is yes.