reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem
  (a 'imp' b) 'imp' (a 'imp' a) = I_el(Y)
proof
  thus (a 'imp' b) 'imp' (a 'imp' a)=(a 'imp' b) 'imp' I_el(Y) by BVFUNC_5:7
    .=I_el(Y) by BVFUNC_6:62;
end;
