reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th18:
  not p,q // p,r1 & p,r1 // p,r2 & q,r1 // q,r2 implies r1=r2
proof
  assume that
A1: ( not p,q // p,r1)& p,r1 // p,r2 and
A2: q,r1 // q,r2;
A3: r1,r2 // r1,q by A2,Th14;
  ( not r1,p // r1,q)& r1,r2 // r1,p by A1,Th14;
  hence thesis by A3,Def1;
end;
