Consider the following premises. Barbara is not writing a letter. For all y, y is a server if and only if y will write a letter. If Barbara were a server, then Barbara is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Barbara is a server.
 From the fact that for all y, y is a server if and only if y will write a letter we can infer that Barbara is a server if and only if Barbara is writing a letter via universal instantiation. From the fact that Barbara is a server if and only if Barbara is writing a letter we can infer that if Barbara writes a letter, then Barbara is a server via biconditional elimination. From the fact that if Barbara were a server, then Barbara is writing a letter, and that if Barbara writes a letter, then Barbara is a server we can infer that Barbara is a server if and only if Barbara is writing a letter via biconditional introduction. Finally, from the fact that Barbara is a server if and only if Barbara is writing a letter, and that Barbara is not writing a letter we can infer that Barbara is not a server via biconditional elimination, which contradicts that Barbara is a server. Therefore, the answer is no.