reserve X for BCI-algebra;
reserve x,y,z for Element of X;
reserve i,j,k,l,m,n for Nat;
reserve f,g for sequence of the carrier of X;

theorem Th37:
  X is BCI-algebra of 0,0,0,0 iff X is BCK-algebra of 0,0,0,0
proof
  thus X is BCI-algebra of 0,0,0,0 implies X is BCK-algebra of 0,0,0,0
  proof
    assume
A1: X is BCI-algebra of 0,0,0,0;
    then X is BCI-algebra of 0,0,0+0,0+0;
    then reconsider X as BCK-algebra by Th36;
    for x,y being Element of X holds Polynom (0,0,x,y) = Polynom (0,0,y,x)
    by A1,Def3;
    hence thesis by Def3;
  end;
  thus thesis;
end;
