Venn diagrams are usually considered to be a method for visualising set-theoretic identities and suggesting true theorems. It is frowned upon to prove a set-theoretic identity using them, such proofs being considered non-rigorous. One of the better kept secrets of the trade is that they can be made rigorous by proving the right kind of ‘metatheorem’. A proof is quite instructive, and might be of interest to set-theoretically minded sixth formers.