I am trying to understand the paper Classical Lambda Calculus in Modern Dress. On page 7, it states
Proposition 2.9 shows inter alia that the products of the universal are dense, and so familiar arguments allow one to deduce more structure. Proposition 2.11 PT is a topos; in particular it is locally cartesian closed.
I believe this means that the subcategory consisting of the objects $ T^m $ for all $ m $ is dense in the category $ PT $, and that we can deduce from this that $ PT $ is a topos (and then from this that it is locally cartesian closed, and therefore has exponentials).
However, I cannot see how one would easily deduce that $ PT $ is a topos, from the fact that we have this dense subcategory. I asked chatGPT, and it mentioned that the dense subcategory can maybe help construct exponentials, which helps in proving that $ PT $ is a topos, but that is the wrong way around.
Can someone shed a bit of light on the issue: what would be the main parts of the "familiar arguments"?