reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;
reserve G for IncProjectivePlane;
reserve a,q for POINT of G;
reserve A,B for LINE of G;

theorem Th24:
  A <> B implies A*B on A & A*B on B & A*B = B*A & (a on A & a on
  B implies a=A*B)
proof
  assume
A1: A <> B;
  then A*B on A,B by Def9;
  then A*B on B,A;
  hence A*B on A & A*B on B & A*B = B*A by A1,Def9;
  assume a on A & a on B;
  then a on A,B;
  hence thesis by A1,Def9;
end;
