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

theorem Th2:
  a 'imp' b = 'not' b 'imp' 'not' a
proof
  (a 'imp' b) 'imp' ('not' b 'imp' 'not' a)=I_el(Y) by BVFUNC_5:32;
  then
A1: a 'imp' b '<' 'not' b 'imp' 'not' a by BVFUNC_1:16;
  ('not' b 'imp' 'not' a) 'imp' (a 'imp' b)=I_el(Y) by BVFUNC_5:31;
  then ('not' b 'imp' 'not' a) '<' (a 'imp' b) by BVFUNC_1:16;
  hence thesis by A1,BVFUNC_1:15;
end;
