Consider the following premises. u_2 <-> p. q <-> u_2. p_1 -> p. Can we infer ~(p_1 -> q) from them? If possible, name the inference rules being used at each step.
 From u_2 <-> p we can infer p -> u_2 via biconditional elimination. From q <-> u_2 we can infer u_2 -> q via biconditional elimination. From p_1 -> p, p -> u_2 we can infer p_1 -> u_2 via transitivity. Finally, from p_1 -> u_2, u_2 -> q we can infer p_1 -> q via transitivity, which contradicts ~(p_1 -> q). Therefore, the answer is no.