Consider the following premises. If Sarah were a police officer, then Elisabeth is sleeping. John is an astronaut if and only if Elisabeth is sleeping. If John were an astronaut, then Thomas is an artist. Can we infer the following from them? If we can, name the inference rule being used: The fact that Sarah were a police officer does not imply that Thomas is an artist.
 From the fact that John is an astronaut if and only if Elisabeth is sleeping we can infer that if Elisabeth sleeps, then John is an astronaut via biconditional elimination. From the fact that if Elisabeth sleeps, then John is an astronaut, and that if John were an astronaut, then Thomas is an artist we can infer that if Elisabeth sleeps, then Thomas is an artist via transitivity. Finally, from the fact that if Sarah were a police officer, then Elisabeth is sleeping, and that if Elisabeth sleeps, then Thomas is an artist we can infer that if Sarah were a police officer, then Thomas is an artist via transitivity, which contradicts that The fact that Sarah were a police officer does not imply that Thomas is an artist. Therefore, the answer is no.