Translate the following inference to logic notation: For all x, x_7 is a bartender if and only if x_7 will drive a car. For all x, if x_7 climbs a mountain, then x_7 is a doctor. For all x, if x_7 drives a car, then x_7 is climbing a mountain. Therefore for all x, if x_7 were a bartender, then x_7 is a doctor.
forall x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) -> S(x).