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

theorem
  a = (a 'imp' b) 'imp' a
proof
  ((a 'imp' b) 'imp' a) 'imp' a = I_el(Y) by BVFUNC_6:100;
  then
A1: ((a 'imp' b) 'imp' a) '<' a by BVFUNC_1:16;
  a 'imp' ((a 'imp' b) 'imp' a) = I_el(Y) by Th32;
  then a '<' ((a 'imp' b) 'imp' a) by BVFUNC_1:16;
  hence thesis by A1,BVFUNC_1:15;
end;
