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