ðˈʌs ðɪ ˈoʊnli ˈɔːltɚnˌeɪɾɪŋ mˌʌltɪlˈɪnɪɹ fˈʌŋkʃənz wɪð ɑːɹ ɹᵻstɹˈɪktᵻd tə ðə fˈʌŋkʃən dᵻfˈaɪnd baɪ ðə lˈeɪbnɪz fˈɔːɹmjʊlə, ænd ɪɾ ɪn fˈækt ˈɔːlsoʊ hɐz ðiːz θɹˈiː pɹˈɑːpɚɾiz.
Thus the only alternating multilinear functions with  are restricted to the function defined by the Leibniz formula, and it in fact also has these three properties.