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