diff --git a/lisp/emacs-lisp/package.el b/lisp/emacs-lisp/package.el
index f92afe56b76..5a79c277f0d 100644
--- a/lisp/emacs-lisp/package.el
+++ b/lisp/emacs-lisp/package.el
@@ -797,6 +797,14 @@ package-built-in-p
         (require 'finder-inf nil t) ; For `package--builtins'.
         (assq package package--builtins))))))
 
+(defun package-core-p (package)
+  "Return non-nil the built-in version of PACKAGE is loaded."
+  (let ((package (if (package-desc-p package)
+                     (package-desc-name package)
+                   package)))
+    (and (assq package (package--alist))
+         (package-built-in-p package))))
+
 (defun package--autoloads-file-name (pkg-desc)
   "Return the absolute name of the autoloads file, sans extension.
 PKG-DESC is a `package-desc' object."
@@ -1908,7 +1916,7 @@ package-compute-transaction
                  (package-version-join (package-desc-version already)))))
       (cond
        (already nil)
-       ((package-installed-p next-pkg next-version) nil)
+       ((package-core-p (car next-pkg))) ;done
 
        (t
         ;; A package is required, but not installed.  It might also be
@@ -2205,11 +2213,9 @@ package-install
      (package--archives-initialize)
      (list (intern (completing-read
                     "Install package: "
-                    (delq nil
-                          (mapcar (lambda (elt)
-                                    (unless (package-installed-p (car elt))
-                                      (symbol-name (car elt))))
-                                  package-archive-contents))
+                    (seq-filter
+                     (lambda (elt) (package-core-p (car elt)))
+                     package-archive-contents)
                     nil t))
            nil)))
   (package--archives-initialize)