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

theorem
  (a 'imp' b) 'or' (a 'imp' 'not' b) = I_el(Y)
proof
  (a 'imp' b) 'or' (a 'imp' 'not' b) =('not' a 'or' b) 'or' (a 'imp' 'not'
  b) by BVFUNC_4:8
    .=('not' a 'or' b) 'or' ('not' a 'or' 'not' b) by BVFUNC_4:8
    .='not' a 'or' (b 'or' ('not' b 'or' 'not' a)) by BVFUNC_1:8
    .='not' a 'or' ((b 'or' 'not' b) 'or' 'not' a) by BVFUNC_1:8
    .='not' a 'or' (I_el(Y) 'or' 'not' a) by BVFUNC_4:6
    .='not' a 'or' I_el(Y) by BVFUNC_1:10;
  hence thesis by BVFUNC_1:10;
end;
