diff --git a/doc/manual/builtins.xml b/doc/manual/builtins.xml
index 1f881a911..3eee36f2a 100644
--- a/doc/manual/builtins.xml
+++ b/doc/manual/builtins.xml
@@ -77,18 +77,8 @@ attrValues = attrs: map (name: builtins.getAttr name attrs) (builtins.attrNames
 if builtins ? getEnv then builtins.getEnv "PATH" else ""</programlisting>
 
     This allows a Nix expression to fall back gracefully on older Nix
-    installations that don’t have the desired built-in function.
-    However, in that case you should not write
-
-<programlisting>
-if builtins ? getEnv then __getEnv "PATH" else ""</programlisting>
-
-    This Nix expression will trigger an “undefined variable” error on
-    older Nix versions since <function>__getEnv</function> doesn’t
-    exist.  <literal>builtins.getEnv</literal>, on the other hand, is
-    safe since <literal>builtins</literal> always exists and attribute
-    selection is lazy, so it’s only performed if the test
-    succeeds.</para></listitem>
+    installations that don’t have the desired built-in
+    function.</para></listitem>
 
   </varlistentry>
 
diff --git a/doc/manual/opt-common.xml b/doc/manual/opt-common.xml
index 316ad6658..ac967e23d 100644
--- a/doc/manual/opt-common.xml
+++ b/doc/manual/opt-common.xml
@@ -251,14 +251,14 @@
 
 <programlisting>
 { # The system (e.g., `i686-linux') for which to build the packages.
-  system ? __currentSystem
+  system ? builtins.currentSystem
   <replaceable>...</replaceable>
 }: <replaceable>...</replaceable></programlisting>
 
   So if you call this Nix expression (e.g., when you do
   <literal>nix-env -i <replaceable>pkgname</replaceable></literal>),
   the function will be called automatically using the value <link
-  linkend='builtin-currentSystem'><literal>__currentSystem</literal></link>
+  linkend='builtin-currentSystem'><literal>builtins.currentSystem</literal></link>
   for the <literal>system</literal> argument.  You can override this
   using <option>--arg</option>, e.g., <literal>nix-env -i
   <replaceable>pkgname</replaceable> --arg system