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<?php
//* Do NOT include the opening php tag shown above. Copy the code shown below.

// add category nicenames in body and post class
function category_id_class( $classes ) {
    global $post;
    foreach ( get_the_category( $post->ID ) as $category ) {
        $classes[] = $category->category_nicename;
    }
    return $classes;
}
add_filter( 'post_class', 'category_id_class' );
add_filter( 'body_class', 'category_id_class' );