Plugin Error (already declared)

Hi there

Can someone explain me, why the following test code already generates an error (…previously declared…)?

if ( ! function_exists( 'mod_footer_admin' ) ) {
  function mod_footer_admin() {
    echo 'My static footer text goes here';
  }
}
add_filter('admin_footer_text', 'mod_footer_admin');

I am new to plugin development and in order to avoid issues with other plugins I created a simple test, which already throws that error at me that I tried to test/avoid:

1. In my themes function.php I am calling that function to modify the footer
2. In my plugin I created exactly that function again to see if the function from the plugin will be ignored (as expected as themes function.php seems to have the higher priority)

Unfortunately I am receiving the error:
Fatal error: Cannot redeclare remove_footer_admin() (previously declared in .../mypluginname_plugin.php:26) in /srv/www/.../functions.php on line 26

I expected that if ( ! function_exists... will add a function unless its already defined and though if it is defined it won`t break the page = ignored?