reserve X for non empty BCIStr_1;
reserve d for Element of X;
reserve n,m,k for Nat;
reserve f for sequence of  the carrier of X;

theorem
  X is BCI-algebra & (for x,y being Element of X holds ((x*y)\x <= y &
  for t being Element of X st t\x <= y holds t <= (x*y))) iff X is
  BCI-Algebra_with_Condition(S) by Lm2,Lm3;
