Consider the following premises. For all x_10, if x_10 sleeps, then x_10 is a carpenter. Elisabeth is sleeping if and only if Robert is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: If Robert were a lawyer, then Elisabeth is a carpenter.
 From the fact that for all x_10, if x_10 sleeps, then x_10 is a carpenter we can infer that if Elisabeth sleeps, then Elisabeth is a carpenter via universal instantiation. From the fact that Elisabeth is sleeping if and only if Robert is a lawyer we can infer that if Robert were a lawyer, then Elisabeth is sleeping via biconditional elimination. Finally, from the fact that if Robert were a lawyer, then Elisabeth is sleeping, and that if Elisabeth sleeps, then Elisabeth is a carpenter we can infer that if Robert were a lawyer, then Elisabeth is a carpenter via transitivity. Therefore, the answer is yes.