How does an HTTP proxy work as a firewall?

The proxy works on the client side of the firewall.

The client is part of a network secured by the firewall and the server is external to the secured network.

The server is connected to a network protected by a firewall with the client external to the network.

The client must authenticate itself to the proxy, which can then pass the request to the server.

Only (1), (2) and (4)