Consider the following premises. t_3 -> t. ~t. t_3 -> t_4. t_3 <-> p. t_4 -> p. Can we infer p from them? If possible, name the inference rules being used at each step.
 From t_3 <-> p we can infer p -> t_3 via biconditional elimination. From t_3 -> t_4, t_4 -> p we can infer t_3 -> p via transitivity. From p -> t_3, t_3 -> p we can infer p <-> t_3 via biconditional introduction. From t_3 -> t, ~t we can infer ~t_3 via modus tollens. Finally, from p <-> t_3, ~t_3 we can infer ~p via biconditional elimination, which contradicts p. Therefore, the answer is no.