Translate the following inference to logic notation: For all x, if x_12 makes tea, then x_12 is a soldier. There is at least one x for which x_12 will make tea if and only if x_12 is a doctor. For all x, if x_12 were a soldier, then x_12 is a doctor. Therefore there is at least one x for which if x_12 were a soldier, then x_12 is a doctor.
forall x: P(x) -> Q(x). exists x: P(x) <-> R(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) -> R(x).