diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index e7027a52ce..65ad323786 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -359,24 +359,29 @@ add_filter( 'style_loader_src', 'wp_style_loader_src', 10, 2 );
 add_action( 'init', 'create_initial_taxonomies', 0 ); // highest priority
 
 // Update
-add_action( 'admin_init', '_maybe_update_core' );
-add_action( 'wp_version_check', 'wp_version_check' );
-add_action( 'upgrader_process_complete', 'wp_version_check', 10, 0 );
-add_action( 'load-plugins.php', 'wp_update_plugins' );
-add_action( 'load-update.php', 'wp_update_plugins' );
-add_action( 'load-update-core.php', 'wp_update_plugins' );
-add_action( 'admin_init', '_maybe_update_plugins' );
-add_action( 'wp_update_plugins', 'wp_update_plugins' );
-add_action( 'upgrader_process_complete', 'wp_update_plugins', 10, 0 );
-add_action( 'load-themes.php', 'wp_update_themes' );
-add_action( 'load-update.php', 'wp_update_themes' );
-add_action( 'load-update-core.php', 'wp_update_themes' );
-add_action( 'admin_init', '_maybe_update_themes' );
-add_action( 'wp_update_themes', 'wp_update_themes' );
-add_action( 'upgrader_process_complete', 'wp_update_themes', 10, 0 );
-add_action( 'update_option_WPLANG', 'wp_clean_update_cache' , 10, 0 );
-add_action( 'wp_maybe_auto_update', 'wp_maybe_auto_update' );
-add_action( 'init', 'wp_schedule_update_checks' );
+if ( ( is_main_site() || is_network_admin() ) && ! ( defined( 'DOING_AJAX' ) && DOING_AJAX ) ) {
+	add_action( 'admin_init',                '_maybe_update_core'              );
+	add_action( 'wp_version_check',          'wp_version_check'                );
+	add_action( 'upgrader_process_complete', 'wp_version_check',         10, 0 );
+
+	add_action( 'load-plugins.php',          'wp_update_plugins'               );
+	add_action( 'load-update.php',           'wp_update_plugins'               );
+	add_action( 'load-update-core.php',      'wp_update_plugins'               );
+	add_action( 'admin_init',                '_maybe_update_plugins'           );
+	add_action( 'wp_update_plugins',         'wp_update_plugins'               );
+	add_action( 'upgrader_process_complete', 'wp_update_plugins',        10, 0 );
+
+	add_action( 'load-themes.php',           'wp_update_themes'                );
+	add_action( 'load-update.php',           'wp_update_themes'                );
+	add_action( 'load-update-core.php',      'wp_update_themes'                );
+	add_action( 'admin_init',                '_maybe_update_themes'            );
+	add_action( 'wp_update_themes',          'wp_update_themes'                );
+	add_action( 'upgrader_process_complete', 'wp_update_themes',         10, 0 );
+
+	add_action( 'update_option_WPLANG',      'wp_clean_update_cache',    10, 0 );
+	add_action( 'wp_maybe_auto_update',      'wp_maybe_auto_update'            );
+	add_action( 'init',                      'wp_schedule_update_checks'       );
+}
 
 // Canonical
 add_action( 'template_redirect', 'redirect_canonical' );
diff --git a/src/wp-includes/update.php b/src/wp-includes/update.php
index c73ee0a32e..e29c78f9a7 100644
--- a/src/wp-includes/update.php
+++ b/src/wp-includes/update.php
@@ -663,7 +663,3 @@ function wp_clean_update_cache() {
 	wp_clean_themes_cache();
 	delete_site_transient( 'update_core' );
 }
-
-if ( ( ! is_main_site() && ! is_network_admin() ) || ( defined( 'DOING_AJAX' ) && DOING_AJAX ) ) {
-	return;
-}