Translate the following inference to logic notation: For all x, x_5 will play tennis. There is at least one x for which if x_5 plays tennis, then x_5 is a doctor. For all x, x_5 will read a book if and only if x_5 is a doctor. Therefore there is at least one x for which x_5 is a doctor.
forall x: P(x). exists x: P(x) -> Q(x). forall x: R(x) <-> Q(x). Therefore exists x: Q(x).