Consider the following premises. q_4 <-> w_1. t -> q_4. q_4 -> t. w_1 -> q_4. ~t. Can we infer ~w_1 from them? If possible, name the inference rules being used at each step.
 From q_4 -> t, t -> q_4 we can infer q_4 <-> t via biconditional introduction. From q_4 <-> w_1 we can infer q_4 -> w_1 via biconditional elimination. From q_4 -> w_1, w_1 -> q_4 we can infer q_4 <-> w_1 via biconditional introduction. From q_4 <-> t, ~t we can infer ~q_4 via biconditional elimination. Finally, from q_4 <-> w_1, ~q_4 we can infer ~w_1 via biconditional elimination. Therefore, the answer is yes.