Consider the following premises. Patricia is a server if and only if Richard is fast. For all x_20, if x_20 were a taxi driver, then x_20 is a server. Patricia is a taxi driver if and only if James is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: If James were an astronaut, then Richard is fast.
 From the fact that for all x_20, if x_20 were a taxi driver, then x_20 is a server we can infer that if Patricia were a taxi driver, then Patricia is a server via universal instantiation. From the fact that Patricia is a taxi driver if and only if James is an astronaut we can infer that if James were an astronaut, then Patricia is a taxi driver via biconditional elimination. From the fact that if James were an astronaut, then Patricia is a taxi driver, and that if Patricia were a taxi driver, then Patricia is a server we can infer that if James were an astronaut, then Patricia is a server via transitivity. From the fact that Patricia is a server if and only if Richard is fast we can infer that if Patricia were a server, then Richard is fast via biconditional elimination. Finally, from the fact that if James were an astronaut, then Patricia is a server, and that if Patricia were a server, then Richard is fast we can infer that if James were an astronaut, then Richard is fast via transitivity. Therefore, the answer is yes.