reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;

theorem
  a,b // c,d & a,c // b9,d implies b = b9
proof
  assume that
A1: a,b // c,d and
A2: a,c // b9,d;
  a,c // b,d by A1,Def1;
  then b,d // a,c by Th3;
  then
A3: d,b // c,a by Th7;
  b9,d // a,c by A2,Th3;
  then d,b9 // c,a by Th7;
  then d,b // d,b9 by A3,Def1;
  hence thesis by Th4;
end;
