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;
