reserve X for BCI-algebra;
reserve X1 for non empty Subset of X;
reserve A,I for Ideal of X;
reserve x,y,z for Element of X;
reserve a for Element of A;

theorem
  I is associative-ideal of X implies for x being Element of X holds x\(
  0.X\x) in I
proof
  assume
A1: I is associative-ideal of X;
  let x be Element of X;
  x\x = 0.X by BCIALG_1:def 5;
  then
A2: (x\0.X)\x =0.X by BCIALG_1:2;
  0.X in I by A1,Def4;
  hence thesis by A1,A2,Th15;
end;
