Consider the following premises. John is playing squash. For all z_4, z_4 will write a letter if and only if z_4 will play squash. For all x, x will sleep. Can we infer the following from them? If we can, name the inference rule being used: John is writing a letter and Richard is sleeping.
 From the fact that for all x, x will sleep we can infer that Richard is sleeping via universal instantiation. From the fact that for all z_4, z_4 will write a letter if and only if z_4 will play squash we can infer that John is writing a letter if and only if John is playing squash via universal instantiation. From the fact that John is writing a letter if and only if John is playing squash we can infer that if John plays squash, then John is writing a letter via biconditional elimination. From the fact that if John plays squash, then John is writing a letter, and that John is playing squash we can infer that John is writing a letter via modus ponens. Finally, from the fact that John is writing a letter, and that Richard is sleeping we can infer that John is writing a letter and Richard is sleeping via conjunction. Therefore, the answer is yes.