Consider the following premises. For all x_3, if x_3 works, then x_3 is excited. For all x_3, if x_3 were excited, then x_3 is working. For all x_3, if x_3 were excited, then x_3 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will work if and only if x_3 is excited.
We can infer this via the universal biconditional introduction rule. Therefore, the answer is yes.