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 Th30:
  PSym(p,a) = PSym(p,b) implies a = b
proof
  assume
A1: PSym(p,a) = PSym(p,b);
  PSym(p,PSym(p,a)) = a by Th29;
  hence thesis by A1,Th29;
end;
