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

theorem Th18:
  for a,b being Function of Y,BOOLEAN holds a 'eqv' b = (a
  'or' 'not' b) '&' ('not' a 'or' b)
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'or' 'not' b) '&' ('not' a 'or' b)).x =((a 'or' 'not' b) '&' (a
    'imp' b)).x by BVFUNC_4:8
      .=((a 'imp' b) '&' (b 'imp' a)).x by BVFUNC_4:8
      .=(a 'eqv' b).x by BVFUNC_4:7;
    hence thesis;
end;
