Consider the following premises. If Charles climbs a mountain, then it is snowing. If Barbara sleeps, then William is reading a book. If William were a mechanic, then Charles is climbing a mountain. For all x_20, if x_20 reads a book, then x_20 is a mechanic. If it snows, then Barbara is sleeping. Can we infer the following from them? If we can, name the inference rule being used: William is reading a book if and only if Charles is climbing a mountain.
 From the fact that for all x_20, if x_20 reads a book, then x_20 is a mechanic we can infer that if William reads a book, then William is a mechanic via universal instantiation. From the fact that if Charles climbs a mountain, then it is snowing, and that if it snows, then Barbara is sleeping we can infer that if Charles climbs a mountain, then Barbara is sleeping via transitivity. From the fact that if William reads a book, then William is a mechanic, and that if William were a mechanic, then Charles is climbing a mountain we can infer that if William reads a book, then Charles is climbing a mountain via transitivity. From the fact that if Charles climbs a mountain, then Barbara is sleeping, and that if Barbara sleeps, then William is reading a book we can infer that if Charles climbs a mountain, then William is reading a book via transitivity. Finally, from the fact that if William reads a book, then Charles is climbing a mountain, and that if Charles climbs a mountain, then William is reading a book we can infer that William is reading a book if and only if Charles is climbing a mountain via biconditional introduction. Therefore, the answer is yes.