Consider the following premises. forall x_10: Q_10(x_10) -> P_10(x_10). exists x_10: P_10(x_10) -> Q_10(x_10). forall x_10: P_10(x_10) or ~Q_10(x_10). Can we infer exists x_10: P_10(x_10) <-> Q_10(x_10) from them? If possible, name the inference rules being used at each step.
We can infer exists x_10: P_10(x_10) <-> Q_10(x_10) via the existential biconditional introduction rule. Therefore, the answer is yes.