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 Th66:
  Collinear a,b,x & Collinear c,d,x & b <> x & c <> x implies
  a,b,c,d are_coplanar
  proof
    assume Collinear a,b,x & Collinear c,d,x & b <> x & c <> x;
    then Collinear b,a,x & Collinear c,d,x & b <> x & c <> x by GTARSKI3:14;
    hence thesis by Th65;
  end;
