Translate the following inference to logic notation: For all x, x_7 is a doctor if and only if x_7 is a writer. For all x, if x_7 were a mechanic, then x_7 is a doctor. There is at least one x for which if x_7 were a writer, then x_7 is a mechanic. Therefore there is at least one x for which if x_7 were a doctor, then x_7 is a writer.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> R(x). Therefore exists x: P(x) -> Q(x).