The user must authenticate to two consecutive firewalls to reach the resource.

fw0fw1.php

<?php
// composer require silex/silex symfony/security && php -S localhost:8888 -t $(pwd)
require 'vendor/autoload.php';

use Silex\Application;
use Silex\Provider\SessionServiceProvider;
use Silex\Provider\SecurityServiceProvider;
use Symfony\Component\HttpFoundation\Response;
use Symfony\Component\HttpFoundation\RedirectResponse;

$app = new Application();

$app->register(new SessionServiceProvider());
$app->register(new SecurityServiceProvider(), [
    'security.firewalls' => [
        'fw1' => [
            'pattern' => '/fw0/fw1',
            'users' => [
                'fw1' => [
                    ['ROLE_USER'],
                    '$2y$13$l3VH4WG.qslkCBw5pB1scOxKXzBdaGwxr4w68B2TwCGIf.bSDNfo6' // fw1
                ]
            ],
            'form' => [
                'default_target_path' => '/fw0/fw1',
                'login_path'          => '/fw0/login_fw1',
                'check_path'          => '/fw0/fw1/login_check',
            ],
            'logout' => [
                'logout_path'        => '/fw0/fw1/logout_fw1',
                'target_url'         => '/fw0/login_fw1',
                'invalidate_session' => false
            ]
        ],
        'fw0' => [
            'pattern' => '/fw0',
            'users' => [
                'fw0' => [
                    ['ROLE_USER'],
                    '$2y$13$j9tSz8zI9KN95GHErFfOC.1cb8.wQ0hixzAPnlMe.UvDimACtEKOq' // fw0
                ]
            ],
            'form' => [
                'default_target_path' => '/fw0',
                'login_path'          => '/login_fw0',
                'check_path'          => '/fw0/login_check',
            ],
            'logout' => [
                'logout_path' => '/fw0/logout_fw0',
                'target_url'  => '/login_fw0'
            ]
        ]
    ]
]);

$app->get('/', function () use ($app) {
    return new RedirectResponse('/login_fw0');
});

$app->get('/login_fw0', function () use ($app) {
    return new Response(<<<EOT
<h4>fw0_login</h4>
<form method="post" action="/fw0/login_check">
    <label for="username">Username</label><br><input id="username" name="_username" value="fw0"><br>
    <label for="password">Password</label><br><input id="password" name="_password" value="fw0"><br>
    <button type="submit">Submit</button>
</form>
EOT
    );
});

$fw1 = function () use ($app) {
    $user = $app['user'];

    return new Response(<<<EOT
Welcome {$user->getUsername()}. <a href="/fw0/logout_fw0">Logout</a>.
<h4>fw1_login</h4>
<form method="post" action="/fw0/fw1/login_check">
    <label for="username">Username</label><br><input id="username" name="_username" value="fw1"><br>
    <label for="password">Password</label><br><input id="password" name="_password" value="fw1"><br>
    <button type="submit">Submit</button>
</form>
EOT
    );
};

$app->get('/fw0', $fw1);
$app->get('/fw0/login_fw1', $fw1);

$app->get('/fw0/fw1', function () use ($app) {
    $user = $app['user'];

    return new Response(<<<EOT
Welcome {$user->getUsername()}. <a href="/fw0/fw1/logout_fw1">Logout</a>.
<h2>Congratulations!</h2>
EOT
    );
});

$app->run();

👍