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 Th69:
  not Collinear a,b,c implies Plane(a,b,c) is_plane & a in Plane(a,b,c) &
  b in Plane(a,b,c) & c in Plane(a,b,c) & (for u,v being POINT of S st
  u in Plane(a,b,c) & v in Plane(a,b,c) & u <> v holds
  Line(u,v) c= Plane(a,b,c))
  proof
    assume not Collinear a,b,c;
    then ex E be Subset of S st Plane(a,b,c) = E & E is_plane & a in E &
      b in E & c in E by Th49;
    hence thesis by Th46;
  end;
