reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem Th5:
  x,y // z,t & x,y // t,z implies x=y or z=t
proof
  assume that
A1: x,y // z,t & x,y // t,z & x<>y and
A2: z<>t;
  z,t // t,z by A1,ANALOAF:def 5;
  hence contradiction by A2,ANALOAF:def 5;
end;
