Consider the following premises. forall x: U_3(x) -> P(x). U_3(a_15) or ~u. P(a_15) -> u. Can we infer ~(U_3(a_15) <-> u) from them? If possible, name the inference rules being used at each step.
 From forall x: U_3(x) -> P(x) we can infer U_3(a_15) -> P(a_15) via universal instantiation. From U_3(a_15) or ~u we can infer u -> U_3(a_15) via rewriting. From U_3(a_15) -> P(a_15), P(a_15) -> u we can infer U_3(a_15) -> u via transitivity. Finally, from U_3(a_15) -> u, u -> U_3(a_15) we can infer U_3(a_15) <-> u via biconditional introduction, which contradicts ~(U_3(a_15) <-> u). Therefore, the answer is no.