A 2-categorical proof of Frobenius for fibrations defined from a generic point

Consider a locally cartesian closed category with an object $\mathbb{I}$ and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential with the generic point of $\mathbb{I}$ defines a trivial fibration. Then the fibrations are also closed under pushforward.