Consider the following premises. It is raining or Linda is not bored. Linda is bored if and only if it is raining. For all x_1, x_1 is not bored. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_1, x_1 is not bored we can infer that Linda is not bored via universal instantiation. From the fact that it is raining or Linda is not bored we can infer that if Linda were bored, then it is raining via rewriting. From the fact that Linda is bored if and only if it is raining we can infer that if it rains, then Linda is bored via biconditional elimination. From the fact that if Linda were bored, then it is raining, and that if it rains, then Linda is bored we can infer that Linda is bored if and only if it is raining via biconditional introduction. Finally, from the fact that Linda is bored if and only if it is raining, and that Linda is not bored we can infer that it is not raining via biconditional elimination. Therefore, the answer is yes.