reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a '&' 'not' b) 'imp'
  'not' a=I_el(Y) implies (a 'imp' b)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  assume
A1: (a '&' 'not' b) 'imp' 'not' a=I_el(Y);
  for x being Element of Y holds (a 'imp' b).x=TRUE
  proof
    let x be Element of Y;
    ((a '&' 'not' b) 'imp' 'not' a).x=TRUE by A1,BVFUNC_1:def 11;
    then 'not' (a '&' 'not' b).x 'or' ('not' a).x = TRUE by BVFUNC_1:def 8;
    then 'not'( a.x '&' ('not' b).x) 'or' ('not' a).x=TRUE by MARGREL1:def 20
;
    then ('not' a.x 'or' 'not' 'not' b.x) 'or' ('not' a).x=TRUE by
MARGREL1:def 19;
    then ('not' a.x 'or' b.x) 'or' 'not' a.x=TRUE by MARGREL1:def 19;
    then b.x 'or' ('not' a.x 'or' 'not' a.x)=TRUE by XBOOLEAN:4;
    hence thesis by BVFUNC_1:def 8;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
