Consider the following premises. p -> r. p_3 -> p. ~t_2. r -> p_3. t_2 <-> p. Can we infer ~p_3 from them? If possible, name the inference rules being used at each step.
 From t_2 <-> p, ~t_2 we can infer ~p via biconditional elimination. From p -> r, r -> p_3 we can infer p -> p_3 via transitivity. From p -> p_3, p_3 -> p we can infer p <-> p_3 via biconditional introduction. Finally, from p <-> p_3, ~p we can infer ~p_3 via biconditional elimination. Therefore, the answer is yes.