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 Th17:
  not a,b // a,c & a,c // p,r & b,c // p,r implies p=r
proof
  assume that
A1: ( not a,b // a,c)& a,c // p,r and
A2: b,c // p,r;
A3: p,r // b,c by A2,Th6;
  ( not a,c // b,c)& p,r // a,c by A1,Th6,Th14;
  hence thesis by A3,Def1;
end;
