Consider the following premises. Barbara is a doctor if and only if Robert is driving a car. Robert is driving a car if and only if Thomas is sleeping. Can we infer the following from them? The fact that Thomas sleeps does not imply that Barbara is a doctor.
 From the fact that Robert is driving a car if and only if Thomas is sleeping we can infer that if Thomas sleeps, then Robert is driving a car. From the fact that Barbara is a doctor if and only if Robert is driving a car we can infer that if Robert drives a car, then Barbara is a doctor. Finally, from the fact that if Thomas sleeps, then Robert is driving a car, and that if Robert drives a car, then Barbara is a doctor we can infer that if Thomas sleeps, then Barbara is a doctor, which contradicts that The fact that Thomas sleeps does not imply that Barbara is a doctor. Therefore, the answer is no.