reserve X for BCI-algebra;
reserve x,y,z,u,a,b for Element of X;
reserve IT for non empty Subset of X;

theorem
  X is quasi-associative iff for x,y,z being Element of X holds (x\y)\z
  <=x\(y\z)
proof
  thus X is quasi-associative implies for x,y,z being Element of X holds (x\y)
  \z<=x\(y\z)
  proof
    assume X is quasi-associative;
    then for x being Element of X holds x`<=x by Th71;
    hence thesis by Lm19;
  end;
  assume for x,y,z being Element of X holds (x\y)\z<=x\(y\z);
  then for x being Element of X holds x`<=x by Lm19;
  hence thesis by Th71;
end;
