Consider the following premises. w -> q_11. w <-> q. q_11 -> w. Can we infer q_11 -> q from them?
 From w -> q_11, q_11 -> w we can infer w <-> q_11. From w <-> q we can infer w -> q. From w <-> q_11 we can infer q_11 -> w. Finally, from q_11 -> w, w -> q we can infer q_11 -> q. Therefore, the answer is yes.