Wireless bridge and cable modem

I have to move the computers in my apartment, and I had the idea
that wireless will help keep the wires down. Here's the topology I'm
thinking of:

Internet
-> Cable modem
-> Wireless bridge 1
-> Wireless bridge 2
-> Linux router
-> Internal network

So, instead of stringing CAT5 across the apartment to connect the Linux
router to the cable modem, I'd like to use wireless. Is this possible?
Will there be issues with the router doing DHCP with the cable modem
across the wireless bridge?

Thanks.