This is not an is-ought inference, it is instrumental reasoning.Let's try the narrow reading, which I take to be:for all X and q (if all H's ought to do X and q is an H then q ought to do X).p is an H.for all X (if all H's ought to do X then p ought to do X).Assuming ought statements obey first-order logic, this is valid reasoning; however, the conclusion has no normative force.