Consider the following premises. Patricia is a musician. If it rains, then Patricia is a musician. If Patricia were a musician, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that if it rains, then Patricia is a musician, and that if Patricia were a musician, then it is raining we can infer that it is raining if and only if Patricia is a musician via biconditional introduction. From the fact that it is raining if and only if Patricia is a musician we can infer that if Patricia were a musician, then it is raining via biconditional elimination. Finally, from the fact that if Patricia were a musician, then it is raining, and that Patricia is a musician we can infer that it is raining via modus ponens, which contradicts that It is not raining. Therefore, the answer is no.