reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a 'xor' b = 'not'( a 'eqv' b)
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    (a 'xor' b).x =('not' 'not'( ('not' a '&' b) 'or' (a '&' 'not' b))).x
    by BVFUNC_4:9
      .=('not'('not'('not' a '&' b) '&' 'not'( a '&' 'not' b))).x by
BVFUNC_1:13
      .=('not'( ('not' 'not' a 'or' 'not' b) '&' 'not'( a '&' 'not' b))).x
    by BVFUNC_1:14
      .=('not'( (a 'or' 'not' b) '&' ('not' a 'or' 'not' 'not' b))).x by
BVFUNC_1:14
      .=('not'( (b 'imp' a) '&' ('not' a 'or' b))).x by BVFUNC_4:8
      .=('not'( (b 'imp' a) '&' (a 'imp' b))).x by BVFUNC_4:8
      .=('not'( a 'eqv' b)).x by BVFUNC_4:7;
    hence thesis;
end;
