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

theorem
  a 'eqv' b = 'not' a 'eqv' 'not' b
proof
  thus 'not' a 'eqv' 'not' b =('not' a 'imp' 'not' b) '&' ('not' b 'imp' 'not'
  a) by BVFUNC_4:7
    .=(b 'imp' a) '&' ('not' b 'imp' 'not' a) by Th2
    .=(b 'imp' a) '&' (a 'imp' b) by Th2
    .=a 'eqv' b by BVFUNC_4:7;
end;
