As an example of an application of this result, we assume that Ψ is a spin-orbital product. Assume further that a spin-orbital occurs twice (is "doubly occupied") in this product, once with coordinate k and once with coordinate q. Then the product is symmetric under the transposition (k, q) and hence vanishes. Notice that this result gives the original formulation of the Pauli principle : no two electrons can have the same set of quantum numbers (be in the same spin-orbital).