Consider the following premises. U_4(c_3) -> w_3. forall x_2: S(x_2) <-> U_4(x_2). Can we infer S(c_3) -> w_3 from them? If possible, name the inference rules being used at each step.
 From forall x_2: S(x_2) <-> U_4(x_2) we can infer S(c_3) <-> U_4(c_3) via universal instantiation. From S(c_3) <-> U_4(c_3) we can infer S(c_3) -> U_4(c_3) via biconditional elimination. Finally, from S(c_3) -> U_4(c_3), U_4(c_3) -> w_3 we can infer S(c_3) -> w_3 via transitivity. Therefore, the answer is yes.