Consider the following premises. forall x_7: Q_4(x_7) -> Q_7(x_7). exists x_7: Q_7(x_7) -> Q_4(x_7). forall x_7: Q_7(x_7) -> Q_4(x_7). Can we infer exists x_7: Q_4(x_7) <-> Q_7(x_7) from them? If possible, name the inference rules being used at each step.
We can infer exists x_7: Q_4(x_7) <-> Q_7(x_7) via the existential biconditional introduction rule. Therefore, the answer is yes.