Remove all remaining traces of MessageLoopProxy.

chrome/browser/chromeos/drive/fileapi/async_file_util.cc

 // Copyright 2014 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/browser/chromeos/drive/fileapi/async_file_util.h"
 
 #include <utility>
 
 #include "base/callback.h"
 #include "base/files/file_path.h"
@@ skipping 61 matching lines @@
     base::File file,
     const base::Closure& close_callback_on_ui_thread) {
   DCHECK_CURRENTLY_ON(BrowserThread::IO);
 
   // It is necessary to make a closure, which runs on file closing here.
   // It will be provided as a FileSystem::OpenFileCallback's argument later.
   // (crbug.com/259184).
   callback.Run(
       std::move(file),
       base::Bind(&google_apis::RunTaskWithTaskRunner,
-                 BrowserThread::GetMessageLoopProxyForThread(BrowserThread::UI),
+                 BrowserThread::GetTaskRunnerForThread(BrowserThread::UI),
                  close_callback_on_ui_thread));
 }
 
 // Runs CreateOrOpenFile when the error happens.
 void RunCreateOrOpenFileCallbackOnError(
     const AsyncFileUtil::CreateOrOpenCallback& callback,
     base::File::Error error) {
   callback.Run(base::File(error), base::Closure());
 }
 
@@ skipping 353 matching lines @@
                      base::Bind(&RunCreateSnapshotFileCallback, callback))),
       base::Bind(callback,
                  base::File::FILE_ERROR_FAILED,
                  base::File::Info(),
                  base::FilePath(),
                  scoped_refptr<storage::ShareableFileReference>()));
 }
 
 }  // namespace internal
 }  // namespace drive