Consider the following premises. p <-> q. w_4 -> p. q -> w_4. Can we infer p <-> w_4 from them? If possible, name the inference rules being used at each step.
 From p <-> q we can infer p -> q via biconditional elimination. From p -> q, q -> w_4 we can infer p -> w_4 via transitivity. Finally, from p -> w_4, w_4 -> p we can infer p <-> w_4 via biconditional introduction. Therefore, the answer is yes.