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

theorem
  a '&' b = 'not' (a 'imp' 'not' b)
proof
  'not'( a 'imp' 'not' b) 'imp' (a '&' b)=I_el(Y) by BVFUNC_6:35;
  then
A1: 'not'( a 'imp' 'not' b) '<' (a '&' b) by BVFUNC_1:16;
  (a '&' b) 'imp' 'not'( a 'imp' 'not' b)=I_el(Y) by BVFUNC_6:34;
  then (a '&' b) '<' 'not'( a 'imp' 'not' b) by BVFUNC_1:16;
  hence thesis by A1,BVFUNC_1:15;
end;
