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
  (for X being BCI-algebra,x,y being Element of X holds x\(y\x)=x)
  implies X is BCK-algebra
proof
  assume
A1: for X being BCI-algebra,x,y being Element of X holds x\(y\x)=x;
  for z being Element of X holds z` = 0.X
  proof
    let z be Element of X;
    (z \ 0.X )` = 0.X by A1;
    hence thesis by Th2;
  end;
  hence thesis by Def8;
end;
