Consider the following premises. P_2(d) or q. forall y_1: P_2(y_1) -> P(y_1). q -> P(d). forall y_1: P(y_1) -> P_2(y_1). Can we infer P(d) from them?
 From forall y_1: P(y_1) -> P_2(y_1), forall y_1: P_2(y_1) -> P(y_1) we can infer forall y_1: P(y_1) <-> P_2(y_1). From forall y_1: P(y_1) <-> P_2(y_1) we can infer forall y_1: P_2(y_1) -> P(y_1). From forall y_1: P_2(y_1) -> P(y_1) we can infer P_2(d) -> P(d). Finally, from P_2(d) -> P(d), q -> P(d), P_2(d) or q we can infer P(d). Therefore, the answer is yes.