reserve            S for satisfying_CongruenceSymmetry
                         satisfying_CongruenceEquivalenceRelation
                         TarskiGeometryStruct,
         a,b,c,d,e,f for POINT of S;
reserve S for satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_SAS
              TarskiGeometryStruct,
        q,a,b,c,a9,b9,c9,x1,x2 for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve       S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve         S for satisfying_CongruenceIdentity
                      satisfying_SegmentConstruction
                      satisfying_BetweennessIdentity
                      satisfying_Pasch
                      TarskiGeometryStruct,
        a,b,c,d,e for POINT of S;
reserve       S for satisfying_Tarski-model
                    TarskiGeometryStruct,
      a,b,c,d,p for POINT of S;
reserve                   S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d,a9,b9,c9,d9 for POINT of S;
reserve S for satisfying_Tarski-model
              TarskiGeometryStruct,
        a,b,c,d,a9,b9,c9,d9,p,q for POINT of S;
reserve                       S for satisfying_Tarski-model
                                    TarskiGeometryStruct,
        a,b,c,d,e,f,a9,b9,c9,d9 for POINT of S;
reserve p for POINT of S;
reserve r for POINT of S;
reserve x,y for POINT of S;
reserve S for non empty satisfying_Tarski-model TarskiGeometryStruct;
reserve p,q,r,s for POINT of S;
reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
  a,b,p,q for POINT of S;

theorem Satz6p17:
  p in Line(p,q) & q in Line(p,q) & Line(p,q) = Line(q,p)
  proof
    thus p in Line(p,q)
    proof
      Collinear p,q,p by Satz3p1;
      hence thesis;
    end;
    Collinear p,q,q by Satz3p1;
    hence q in Line(p,q);
    thus Line(p,q)=Line(q,p)
    proof
A2:   Line(p,q) c= Line(q,p)
      proof
        let x be object;
        assume x in Line(p,q);
        then consider y be POINT of S such that
A3:     y = x and
A4:     Collinear p,q,y;
        Collinear q,p,y by A4,Satz3p2;
        hence thesis by A3;
      end;
      Line(q,p) c= Line(p,q)
      proof
        let x be object;
        assume x in Line(q,p);
        then consider y be POINT of S such that
A5:     y = x and
A6:     Collinear q,p,y;
        Collinear p,q,y by A6,Satz3p2;
        hence thesis by A5;
      end;
      hence thesis by A2;
    end;
  end;
