Consider the following premises. For all z, z will write a letter if and only if z will sleep. For all z, if z were bored, then z is fast. For all z, if z were fast, then z is writing a letter. 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 bored does not imply that z is sleeping.
 From the fact that for all z, z will write a letter if and only if z will sleep we can infer that for all z, if z writes a letter, then z is sleeping via universal biconditional elimination. From the fact that for all z, if z were fast, then z is writing a letter, and that for all z, if z writes a letter, then z is sleeping we can infer that for all z, if z were fast, then z is sleeping via universal transitivity. Finally, from the fact that for all z, if z were bored, then z is fast, and that for all z, if z were fast, then z is sleeping we can infer that for all z, if z were bored, then z is sleeping via universal transitivity, which contradicts that There is at least one z for which the fact that z were bored does not imply that z is sleeping. Therefore, the answer is no.