In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman’s New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by analyzing an episode from a lesson in set theory taught to prospective secondary mathematics teachers. We suggest that a conscious use of rhetorical figures may enrich proof teaching and support ideas that lecturers consider important to convey to their students.