Pseudo-Canonical Formulae are Classical

From now on a, b, c, x, y, z, A, B, C, X, Y denote sets, f , g denote functions, V denotes a SetValuation, P denotes a permutation of V , p, q, r, s denote elements of HP-WFF, and n denotes an element of N. Let us consider X and Y. Let f be a relation between X and Y. Note that idX · f reduces to f and f · idY reduces to f . Now we state the proposition: (1) Let us consider one-to-one functions f , g. If f−1 = g−1, then f = g.