Consider the following premises. q -> p. p_6 -> q. p <-> p_6. Can we infer ~(p_6 <-> p) from them?
 From p_6 -> q, q -> p we can infer p_6 -> p. From p <-> p_6 we can infer p -> p_6. Finally, from p_6 -> p, p -> p_6 we can infer p_6 <-> p, which contradicts ~(p_6 <-> p). Therefore, the answer is no.