diff --git a/sphinx/builders/dirhtml.py b/sphinx/builders/dirhtml.py
index 5e6b17259..9365889bd 100644
--- a/sphinx/builders/dirhtml.py
+++ b/sphinx/builders/dirhtml.py
@@ -13,7 +13,6 @@ from typing import Any, Dict
 
 from sphinx.application import Sphinx
 from sphinx.builders.html import StandaloneHTMLBuilder
-from sphinx.deprecation import RemovedInSphinx40Warning, deprecated_alias
 from sphinx.util import logging
 from sphinx.util.osutil import SEP, os_path
 
@@ -46,17 +45,6 @@ class DirectoryHTMLBuilder(StandaloneHTMLBuilder):
         return outfilename
 
 
-# for compatibility
-deprecated_alias('sphinx.builders.html',
-                 {
-                     'DirectoryHTMLBuilder':  DirectoryHTMLBuilder,
-                 },
-                 RemovedInSphinx40Warning,
-                 {
-                     'DirectoryHTMLBuilder': 'sphinx.builders.dirhtml.DirectoryHTMLBuilder',
-                 })
-
-
 def setup(app: Sphinx) -> Dict[str, Any]:
     app.setup_extension('sphinx.builders.html')
 
diff --git a/sphinx/builders/singlehtml.py b/sphinx/builders/singlehtml.py
index 03d25965b..13c1c2f86 100644
--- a/sphinx/builders/singlehtml.py
+++ b/sphinx/builders/singlehtml.py
@@ -16,7 +16,6 @@ from docutils.nodes import Node
 
 from sphinx.application import Sphinx
 from sphinx.builders.html import StandaloneHTMLBuilder
-from sphinx.deprecation import RemovedInSphinx40Warning, deprecated_alias
 from sphinx.environment.adapters.toctree import TocTree
 from sphinx.locale import __
 from sphinx.util import logging, progress_message
@@ -187,18 +186,6 @@ class SingleFileHTMLBuilder(StandaloneHTMLBuilder):
             self.handle_page('opensearch', {}, 'opensearch.xml', outfilename=fn)
 
 
-# for compatibility
-deprecated_alias('sphinx.builders.html',
-                 {
-                     'SingleFileHTMLBuilder': SingleFileHTMLBuilder,
-                 },
-                 RemovedInSphinx40Warning,
-                 {
-                     'SingleFileHTMLBuilder':
-                     'sphinx.builders.singlehtml.SingleFileHTMLBuilder',
-                 })
-
-
 def setup(app: Sphinx) -> Dict[str, Any]:
     app.setup_extension('sphinx.builders.html')