theorem Satz7p17:
  Middle p,a,p9 & Middle p,b,p9 implies a = b
  proof
    assume that
A1: Middle p,a,p9 and
A2: Middle p,b,p9;
    now
      thus between p,b,p9 by A2;
      reflection(a,p) = p9 by A1,DEFR;
      then b,p9 equiv reflection(a,b),reflection(a,reflection(a,p))
        by Satz7p13;
      then b,p9 equiv reflection(a,b),p by Satz7p7;
      then b,p equiv reflection(a,b),p by A2,Satz2p3;
      hence p,b equiv reflection(a,b),p by Satz2p4;
      hence p,b equiv p,reflection(a,b) by Satz2p5;
      b,p equiv reflection(a,b),reflection(a,p) by Satz7p13;
      then b,p equiv reflection(a,b),p9 by A1,DEFR;
      then b,p9 equiv reflection(a,b),p9 by A2,GTARSKI1:def 6;
      then p9,b equiv reflection(a,b),p9 by Satz2p4;
      hence p9,b equiv p9,reflection(a,b) by Satz2p5;
    end;
    then reflection(a,b) = b by Satz4p19;
    hence thesis by Satz7p10;
  end;
