Consider the following premises. w_3 -> ~p. p_1 -> w_3. p. p_1 <-> w_1. Can we infer w_1 from them?
 From w_3 -> ~p, p we can infer ~w_3. From p_1 -> w_3, ~w_3 we can infer ~p_1. Finally, from p_1 <-> w_1, ~p_1 we can infer ~w_1, which contradicts w_1. Therefore, the answer is no.