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
  X is BCK-algebra of i,j,m,n iff X is BCK-algebra of m,n,i,j
proof
  thus X is BCK-algebra of i,j,m,n implies X is BCK-algebra of m,n,i,j
  proof
    assume
A1: X is BCK-algebra of i,j,m,n;
    then
    for x,y being Element of X holds Polynom (m,n,x,y) = Polynom (i,j,y,x)
    by Def3;
    hence thesis by A1,Def3;
  end;
  assume
A2: X is BCK-algebra of m,n,i,j;
  then for x,y being Element of X holds Polynom (m,n,y,x) = Polynom (i,j,x,y)
  by Def3;
  hence thesis by A2,Def3;
end;
