Consider the following premises. For all x_11, x_11 is a politician if and only if x_11 is sad. Patricia is not sad. For all z, z is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not a politician and Sarah is an astronaut.
 From the fact that for all z, z is an astronaut we can infer that Sarah is an astronaut via universal instantiation. From the fact that for all x_11, x_11 is a politician if and only if x_11 is sad we can infer that Patricia is a politician if and only if Patricia is sad via universal instantiation. From the fact that Patricia is a politician if and only if Patricia is sad, and that Patricia is not sad we can infer that Patricia is not a politician via biconditional elimination. Finally, from the fact that Patricia is not a politician, and that Sarah is an astronaut we can infer that Patricia is not a politician and Sarah is an astronaut via conjunction. Therefore, the answer is yes.