theorem Th20:
  MABE = <* p1, p2, p5 *> &
  MACF = <* p1, p3, p6 *> &
  MBDF = <* p2, p4, p6 *> &
  MCDE = <* p3, p4, p5 *> &
  MABF = <* p1, p2, p6 *> &
  MACE = <* p1, p3, p5 *> &
  MBDE = <* p2, p4, p5 *> &
  MCDF = <* p3, p4, p6 *> implies
  Det MABE = |{ p1, p2, p5 }| &
  Det MACF = |{ p1, p3, p6 }| &
  Det MBDF = |{ p2, p4, p6 }| &
  Det MCDE = |{ p3, p4, p5 }| &
  Det MABF = |{ p1, p2, p6 }| &
  Det MACE = |{ p1, p3, p5 }| &
  Det MBDE = |{ p2, p4, p5 }| &
  Det MCDF = |{ p3, p4, p6 }|
  proof
    assume that
A1: MABE = <* p1, p2, p5 *> and
A2: MACF = <* p1, p3, p6 *> and
A3: MBDF = <* p2, p4, p6 *> and
A4: MCDE = <* p3, p4, p5 *> and
A5: MABF = <* p1, p2, p6 *> and
A6: MACE = <* p1, p3, p5 *> and
A7: MBDE = <* p2, p4, p5 *> and
A8: MCDF = <* p3, p4, p6 *>;
    p1 = <* p1`1,p1`2,p1`3 *> & p2 = <* p2`1,p2`2,p2`3 *> &
    p3 = <* p3`1,p3`2,p3`3 *> & p4 = <* p4`1,p4`2,p4`3 *> &
    p5 = <* p5`1,p5`2,p5`3 *> & p6 = <* p6`1,p6`2,p6`3 *> by EUCLID_5:3;
    hence thesis by A1,A2,A3,A4,A5,A6,A7,A8,ANPROJ_8:35;
  end;
