reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct;
reserve a,b for POINT of S;
reserve A for Subset of S;
reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct;
reserve a,b,c,m,r,s for POINT of S;
reserve A for Subset of S;
reserve S         for non empty satisfying_Lower_Dimension_Axiom
                                satisfying_Tarski-model
                                TarskiGeometryStruct,
        a,b,c,d,m,p,q,r,s,x for POINT of S,
        A,A9,E              for Subset of S;

theorem Th38:
  A is_line & A9 is_line & A <> A9 implies ex r being POINT of S st
  not r in A & r in A9
  proof
    assume that
A1: A is_line and
A2: A9 is_line and
A3: A <> A9;
    consider p9,q9 be POINT of S such that
A4: p9 <> q9 and
A5: A9 = Line(p9,q9) by A2;
    not (p9 in A & q9 in A) by A1,A3,A4,A5,GTARSKI3:87;
    hence thesis by A5,GTARSKI3:83;
  end;
