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

theorem Th32:
  a 'imp' ((a 'imp' b) 'imp' a) = I_el(Y)
proof
  thus a 'imp' ((a 'imp' b) 'imp' a) ='not' a 'or' ((a 'imp' b) 'imp' a) by
BVFUNC_4:8
    .='not' a 'or' ('not' (a 'imp' b) 'or' a) by BVFUNC_4:8
    .='not' a 'or' ('not' ('not' a 'or' b) 'or' a) by BVFUNC_4:8
    .='not' a 'or' (('not' 'not' a '&' 'not' b) 'or' a) by BVFUNC_1:13
    .=('not' a 'or' a) 'or' (a '&' 'not' b) by BVFUNC_1:8
    .=I_el(Y) 'or' (a '&' 'not' b) by BVFUNC_4:6
    .=I_el(Y) by BVFUNC_1:10;
end;
