TMUTEX在德尔福重新进入市场吗?

我正在创建互斥体:

 FMutex := TMutex.Create(nil, False, 'SomeDumbText');

并在使用相同创建的互斥体调用另一个方法的方法中使用它:

procedure a;
begin
  FMutex.Acquire;
  try
    //do some work here and maybe call b
  finally
    FMutex.Release;
  end;
end;

procedure b;
begin
  FMutex.Acquire;
  try
    //do some work here
  finally
    FMutex.Release;
  end;
end;

有嵌套的互斥体是安全的吗?