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add_filter( 'body_class', 'add_page_slug_class_name' );
function add_page_slug_class_name( $classes ) {
  if ( is_page() ) {
    $page = get_post( get_the_ID() );
    $classes[] = $page->post_name;

    $parent_id = $page->post_parent;
    if ( $parent_id ) {
      $classes[] = get_post($parent_id)->post_name . '-child';
    }
  }
  return $classes;
}