Consider the following premises. For all z, z will play tennis if and only if z is a lawyer. John is not an office clerk. Sarah is not a lawyer. For all x_11, x_11 is happy if and only if x_11 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: John is not happy and Sarah is not playing tennis.
 From the fact that for all z, z will play tennis if and only if z is a lawyer we can infer that Sarah is playing tennis if and only if Sarah is a lawyer via universal instantiation. From the fact that Sarah is playing tennis if and only if Sarah is a lawyer, and that Sarah is not a lawyer we can infer that Sarah is not playing tennis via biconditional elimination. From the fact that for all x_11, x_11 is happy if and only if x_11 is an office clerk we can infer that John is happy if and only if John is an office clerk via universal instantiation. From the fact that John is happy if and only if John is an office clerk, and that John is not an office clerk we can infer that John is not happy via biconditional elimination. Finally, from the fact that John is not happy, and that Sarah is not playing tennis we can infer that John is not happy and Sarah is not playing tennis via conjunction. Therefore, the answer is yes.