wp_nav_menu and conditional nav menu

I have a place in my template that I want to display a specific menu, if it exists, and otherwise not show anything, even if other menus exist.

In my functions.php I have this code:

add_action('init', 'register_custom_menu');
function register_custom_menu() {
	register_nav_menu('navigation', __('Navigation', 'framework'));
}

In the template I have this code to display that menu:

<?php wp_nav_menu(array(
	'menu' => 'navigation',
	'container' => 'nav',
	'container_id' => 'top-nav',
	'fallback_cb' => 'false',
	'depth' => -1
)); ?>

What currently happens: I have two menus, one named “Navigation” and one named “Test”. “Navigation” shows where the above code is in the template, and “Test” is in a widget in the sidebar. If I delete the menu named “Navigation” then the “Test” menu displays where “Navigation” was and also in the widget. What I want is for nothing to display in the “Navigation” spot unless there is a menu named “Navigation”.

I thought by setting fallback_cb to false, if the menu named “Navigation” doesn’t exist, then it will fallback to nothing but that doesn’t seem to be the case. I know there’s probably a way to use an if statement to test if the menu exists, but I was hoping for something more elegant. Am I misunderstanding how wp_nav_menu() works or is there something else I’m missing?

Thanks for your help in advance.