Consider the following premises. If Patricia were a lawyer, then Mary is not running. For all x_7, x_7 is a lawyer if and only if x_7 is a cashier. For all x, x will go running. Can we infer the following from them? If we can, name the inference rule being used: Patricia is a cashier.
 From the fact that for all x, x will go running we can infer that Mary is running via universal instantiation. From the fact that for all x_7, x_7 is a lawyer if and only if x_7 is a cashier we can infer that Patricia is a lawyer if and only if Patricia is a cashier via universal instantiation. From the fact that if Patricia were a lawyer, then Mary is not running, and that Mary is running we can infer that Patricia is not a lawyer via modus tollens. Finally, from the fact that Patricia is a lawyer if and only if Patricia is a cashier, and that Patricia is not a lawyer we can infer that Patricia is not a cashier via biconditional elimination, which contradicts that Patricia is a cashier. Therefore, the answer is no.