Consider the following premises. w or U_4(f_2). w -> S(f_2). forall y: U_4(y) <-> S(y). Can we infer S(f_2) from them? If possible, name the inference rules being used at each step.
 From forall y: U_4(y) <-> S(y) we can infer U_4(f_2) <-> S(f_2) via universal instantiation. From U_4(f_2) <-> S(f_2) we can infer U_4(f_2) -> S(f_2) via biconditional elimination. Finally, from w -> S(f_2), U_4(f_2) -> S(f_2), w or U_4(f_2) we can infer S(f_2) via disjunction elimination. Therefore, the answer is yes.