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
  for X being BCK-algebra of i,j,m,n st i = n holds X is BCK-algebra of i,j,j,i
proof
  let X be BCK-algebra of i,j,m,n;
  assume i = n;
  then reconsider X as BCK-algebra of i,j,m,i;
  for x,y being Element of X holds Polynom (i,j,x,y) = Polynom (j,i,y,x)
  proof
    let x,y be Element of X;
    Polynom (i,j,x,y) = Polynom (m,i,y,x) by Def3;
    hence thesis by Th20;
  end;
  hence thesis by Def3;
end;
