diff --git a/Lib/mailbox.py b/Lib/mailbox.py
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -1874,17 +1874,26 @@
             self._pos = f.tell()
         else:
             self._pos = pos
+        self._do_close = True
+        self._is_open = True
+
+    def _set_noclose(self):
+        """Subclass hook - use to prevent close of file."""
+        self._do_close = False
 
     def read(self, size=None):
         """Read bytes."""
+        self._closed_check()
         return self._read(size, self._file.read)
 
     def read1(self, size=None):
         """Read bytes."""
+        self._closed_check()
         return self._read(size, self._file.read1)
 
     def readline(self, size=None):
         """Read a line."""
+        self._closed_check()
         return self._read(size, self._file.readline)
 
     def readlines(self, sizehint=None):
@@ -1908,10 +1917,12 @@
 
     def tell(self):
         """Return the position."""
+        self._closed_check()
         return self._pos
 
     def seek(self, offset, whence=0):
         """Change position."""
+        self._closed_check()
         if whence == 1:
             self._file.seek(self._pos)
         self._file.seek(offset, whence)
@@ -1919,9 +1930,15 @@
 
     def close(self):
         """Close the file."""
-        if hasattr(self._file, 'close'):
+        if self._do_close:
+            self._do_close = False
             self._file.close()
-        del self._file
+            del self._file
+        self._is_open = False
+
+    def _closed_check(self):
+        if not self._is_open:
+            raise ValueError('I/O operation on closed file')
 
     def _read(self, size, read_method):
         """Read size bytes using read_method."""
@@ -1940,20 +1957,24 @@
         self.close()
 
     def readable(self):
+        self._closed_check()
         return self._file.readable()
 
     def writable(self):
-        return self._file.writable()
+        self._closed_check()
+        return False
 
     def seekable(self):
+        self._closed_check()
         return self._file.seekable()
 
     def flush(self):
+        self._closed_check()
         return self._file.flush()
 
     @property
     def closed(self):
-        return self._file.closed
+        return not self._is_open
 
 
 class _PartialFile(_ProxyFile):
@@ -1962,6 +1983,7 @@
     def __init__(self, f, start=None, stop=None):
         """Initialize a _PartialFile."""
         _ProxyFile.__init__(self, f, start)
+        super()._set_noclose()
         self._start = start
         self._stop = stop
 
@@ -1971,6 +1993,7 @@
 
     def seek(self, offset, whence=0):
         """Change position, possibly with respect to start or stop."""
+        self._closed_check()
         if whence == 0:
             self._pos = self._start
             whence = 1
@@ -1988,11 +2011,6 @@
             size = remaining
         return _ProxyFile._read(self, size, read_method)
 
-    def close(self):
-        # do *not* close the underlying file object for partial files,
-        # since it's global to the mailbox object
-        del self._file
-
 
 def _lock_file(f, dotlock=True):
     """Lock file f using lockf and dot locking."""
diff --git a/Lib/test/test_mailbox.py b/Lib/test/test_mailbox.py
--- a/Lib/test/test_mailbox.py
+++ b/Lib/test/test_mailbox.py
@@ -290,12 +290,14 @@
         key1 = self._box.add(_sample_message)
         with self._box.get_file(key0) as file:
             data0 = file.read()
-        with self._box.get_file(key1) as file:
-            data1 = file.read()
+        file1 = self._box.get_file(key1)
+        data1 = file1.read()
         self.assertEqual(data0.decode('ascii').replace(os.linesep, '\n'),
                          self._template % 0)
         self.assertEqual(data1.decode('ascii').replace(os.linesep, '\n'),
                          _sample_message)
+        file1.close()
+        file1.close()
 
     def test_iterkeys(self):
         # Get keys using iterkeys()
@@ -1834,9 +1836,17 @@
 
     def _test_close(self, proxy):
         # Close a file
+        self.assertFalse(proxy.closed)
         proxy.close()
-        self.assertRaises(AttributeError, lambda: proxy.close())
-
+        self.assertTrue(proxy.closed)
+        self.assertRaises(ValueError, proxy.read)
+        self.assertRaises(ValueError, proxy.read1)
+        self.assertRaises(ValueError, proxy.readlines)
+        self.assertRaises(ValueError, proxy.tell)
+        self.assertRaises(ValueError, proxy.readable)
+        self.assertRaises(ValueError, proxy.writable)
+        self.assertRaises(ValueError, proxy.seekable)
+        self.assertRaises(ValueError, proxy.flush)
 
 class TestProxyFile(TestProxyFileBase):