Consider the following premises. For all z_3, z_3 will go running if and only if z_3 will cook. Thomas is cooking. For all x_25, x_25 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: Thomas is running and Patricia is a cashier.
 From the fact that for all x_25, x_25 is a cashier we can infer that Patricia is a cashier via universal instantiation. From the fact that for all z_3, z_3 will go running if and only if z_3 will cook we can infer that Thomas is running if and only if Thomas is cooking via universal instantiation. From the fact that Thomas is running if and only if Thomas is cooking we can infer that if Thomas cooks, then Thomas is running via biconditional elimination. From the fact that if Thomas cooks, then Thomas is running, and that Thomas is cooking we can infer that Thomas is running via modus ponens. Finally, from the fact that Thomas is running, and that Patricia is a cashier we can infer that Thomas is running and Patricia is a cashier via conjunction. Therefore, the answer is yes.