 reserve S for satisfying_Tarski-model TarskiGeometryStruct;
 reserve a, b, c, d, e, f, o, p, q, r, s,
    v, w, u, x, y, z, a9, b9, c9, d9, x9, y9, z for POINT of S;

theorem CongruenceDoubleSymmetry:
  a,b equiv c,d implies b,a equiv d,c
  proof
X1: b,a equiv a,b & c,d equiv d,c by A1;
    assume a,b equiv c,d; then
    a,b equiv d,c by X1, EquivTransitive;
    hence thesis by X1, EquivTransitive;
  end;
