Consider the following premises. If Robert plays squash, then Mary is sleeping. Linda is rich if and only if Mary is sleeping. If William were a carpenter, then Mary is sleeping. Robert is playing squash or it is overcast. If it is overcast, then William is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Linda is rich.
 From the fact that if it is overcast, then William is a carpenter, and that if William were a carpenter, then Mary is sleeping we can infer that if it is overcast, then Mary is sleeping via transitivity. From the fact that if Robert plays squash, then Mary is sleeping, that if it is overcast, then Mary is sleeping, and that Robert is playing squash or it is overcast we can infer that Mary is sleeping via disjunction elimination. From the fact that Linda is rich if and only if Mary is sleeping we can infer that if Mary sleeps, then Linda is rich via biconditional elimination. Finally, from the fact that if Mary sleeps, then Linda is rich, and that Mary is sleeping we can infer that Linda is rich via modus ponens. Therefore, the answer is yes.