reserve F,H,H9 for ZF-formula,
  x,y,z,t for Variable,
  a,b,c,d,A,X for set;
reserve E for non empty set,
  f,g,h for Function of VAR,E,
  v1,v2,v3,v4,v5,u5 for Element of VAL E;

theorem
  E |= All(x,H) iff E |= H
proof
  thus E |= All(x,H) implies E |= H
  proof
    assume
A1: for f holds E,f |= All(x,H);
    let f;
   for y st f.y <> f.y holds x = y;
   hence thesis by A1,Th16;
  end;
  assume
A2: E |= H;
  let f;
  for g st for y st g.y <> f.y holds x = y holds E,g |= H by A2;
  hence thesis by Th16;
end;
