Consider the following premises. forall x_7: P_7(x_7) -> T(x_7). exists x_7: P_7(x_7) <-> T(x_7). Can we infer exists x_7: P_7(x_7) -> T(x_7) from them? If possible, name the inference rules being used at each step.
 From exists x_7: P_7(x_7) <-> T(x_7) we can infer exists x_7: T(x_7) -> P_7(x_7) via existential biconditional elimination. From exists x_7: T(x_7) -> P_7(x_7), forall x_7: P_7(x_7) -> T(x_7) we can infer exists x_7: T(x_7) <-> P_7(x_7) via existential biconditional introduction. Finally, from exists x_7: T(x_7) <-> P_7(x_7) we can infer exists x_7: P_7(x_7) -> T(x_7) via existential biconditional elimination. Therefore, the answer is yes.