theorem
  I is positive-implicative-ideal of X iff for x,y,z being Element of X
  st (x\y)\z in I holds (x\z)\(y\z) in I
proof
  I is positive-implicative-ideal of X implies for x,y,z being Element of
  X st (x\y)\z in I & y\z in I holds x\z in I by Def8;
  hence thesis by Th52,Th53;
end;
