How to implement a custom customer name validation for the billing addresses?

I have a custom validation rule (custom-firstname) in my rules.js file. In checkout_index_index I’ve set the firstname field to be validated in shipping address form - in the first checkout step that is. It looks like this:

<item name="firstname" xsi:type="array">
    <item name="validation" xsi:type="array">
        <item name="custom-firstname" xsi:type="string">true</item>
    </item>
</item>

How to do the same in billing address - in the second checkout step where user can set up another address? I’m trying to put the billingAddress child to billing-step but it doesnt work.

<item name="billingAddress" xsi:type="array">
    <item name="children" xsi:type="array">
        <item name="billing-address-fieldset" xsi:type="array">
            <item name="children" xsi:type="array">
                <item name="firstname" xsi:type="array">
                    <item name="validation" xsi:type="array">
                        <item name="custom-firstname" xsi:type="string">true</item>
                    </item>
                </item>
            </item>
        </item>
    </item>
</item>