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 Th36:
  PSym(p,a) = PSym(q,a) iff p = q or MDist p,q
proof
A1: now
    assume
A2: MDist p,q;
    Mid a,p,PSym(p,a) & Mid a,q,PSym(q,a) by Def4;
    hence PSym(p,a) = PSym(q,a) by A2,Th24;
  end;
  now
    assume
A3: PSym(p,a) = PSym(q,a);
    Mid a,p,PSym(p,a) & Mid a,q,PSym(q,a) by Def4;
    hence p = q or MDist p,q by A3,Th20;
  end;
  hence thesis by A1;
end;
