Consider the following premises. p_1 -> p_4. p <-> t. p -> p_4. p_1. Can we infer p_4 from them? If possible, name the inference rules being used at each step.
 From p <-> t we can infer t -> p via biconditional elimination. From t -> p, p -> p_4 we can infer t -> p_4 via transitivity. From p_1 we can infer p_1 or t via addition. Finally, from p_1 -> p_4, t -> p_4, p_1 or t we can infer p_4 via disjunction elimination. Therefore, the answer is yes.