reserve Y for non empty set;

theorem Th7:
  for a,b being Function of Y,BOOLEAN
   holds a 'eqv' b = (a 'imp' b) '&' (b 'imp' a)
proof
  let a,b be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'eqv' b).x = a.x <=> b.x by BVFUNC_1:def 9
     .= (a.x => b.x) '&' (b.x => a.x)
     .= (a 'imp' b).x '&' (b.x => a.x) by BVFUNC_1:def 8
     .= (a 'imp' b).x '&' (b 'imp' a).x by BVFUNC_1:def 8
     .= ((a 'imp' b) '&' (b 'imp' a)).x by MARGREL1:def 20;
end;
