let i, j, m, n be Nat; :: thesis: for X being BCK-algebra of i,j,m,n holds X is BCK-algebra of i,j,j,n
let X be BCK-algebra of i,j,m,n; :: thesis: X is BCK-algebra of i,j,j,n
for x, y being Element of X holds Polynom (i,j,x,y) = Polynom (j,n,y,x)

proof

let x, y be Element of X; :: thesis: Polynom (i,j,x,y) = Polynom (j,n,y,x)
Polynom (i,j,x,y) = Polynom (m,n,y,x) by Def3;
hence Polynom (i,j,x,y) = Polynom (j,n,y,x) by Th20; :: thesis: verum

end;

hence X is BCK-algebra of i,j,j,n by Def3; :: thesis: verum