Category of categories with pullbacks is cartesian closed

Dear category theorists, I noticed recently that the category whose objects are categories with pullbacks and whose morphisms are pullback preserving functors is cartesian closed. Given a pair of categories with pullbacks A and B, the internal hom [A,B] has objects: pullback preserving functors from A to B, and morphisms: cartesian natural transformations. I have posted a short paper on the arxiv proving this fact: http://arxiv.org/abs/0904.2486 It seems like a fairly natural fact but is not to my knowledge in the literature. I am wondering whether anyone was previously aware of this result, and if so whether it might be mentioned somewhere in the literature? Thanks, John Bourke, University of Sydney.