Consider the following premises. If David were not a scientist, then Barbara is playing squash. For all x_11, x_11 is a cashier if and only if x_11 is a scientist. David is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: Barbara is playing squash.
 From the fact that for all x_11, x_11 is a cashier if and only if x_11 is a scientist we can infer that David is a cashier if and only if David is a scientist via universal instantiation. From the fact that David is a cashier if and only if David is a scientist, and that David is not a cashier we can infer that David is not a scientist via biconditional elimination. Finally, from the fact that if David were not a scientist, then Barbara is playing squash, and that David is not a scientist we can infer that Barbara is playing squash via modus ponens. Therefore, the answer is yes.