A running commentary is offered on the first half of Frege's Grundlagen der Arithmetik, §17, and suggests that Frege anticipated the method of demonstration used by Paul Bernays for the Deduction Theorem.The Natural Deduction community owes Peter Schroeder-Heister a large debt of gratitude, not only for his seminal extension of the Natural Deduction techniques to higher-level derivations, and as the champion advocate of Proof-Theoretic Semantics.1 He has also been a tireless and successful organizer of successful workshops and conferences at Tübingen that, over the past quarter of a century, have served to put Natural Deduction firmly on the map as a viable alternative for proof-theoretic bookkeeping. It is a pleasure to contribute to a Profile volume devoted to his work, and in his honour. However, by the side of his Natural Deduction expertise, Peter Schroeder-Heister has also followed other lines of research; thus he has also dealt