How to downgrade from the iPhone OS 4.0 beta1/2 to firmware 3.1.3 for Windows & Mac

Not satisfied with the iPhone OS 4.0 beta1/2? Have you tested it and want back to 3.1.3 or lower?
Here`s the guide:

1. Get your iPhone into the DFU mode by turning it off and holding the homebutton by connecting it with the USB cable. If you see the iTunes logo on your screen you can release the homebutton
2. Install the 3.1.3 firmware with iTunes on your device (Press alt while clicking on the restorebutton in iTunes and choose the iPhone 3.1.3_restore.ipsw file manually). The installation will end up with an error
   
3. The OS 4.0 beta1/2 has updated your Baseband to a higher version that 3.1.3 comes with. This results in the "iphone restore error", iTunes says that it needs to be restored each time you connect it
4. Download iRecovery , Mac users skip point 5!
5. Windows only: install libusb-win32-filter-bin-0.1.12.2.exe from the package above. Vista needs to run this file as administrator and in compatibility mode
6. Open Terminal. Type in cd{space} and drag your iRecovery file into the Terminal, before you press enter delete the "iRecovery" textpart at the end
   
7. Type in "iRecovery -s" , sometimes this only works for Mac: "./iRecovery -s"
8. Type in the following commands: "setenv auto-boot true" {enter}, "saveenv" {enter},
   "exit" {enter}
9. Restart your device

After the reboot you have successfully downgraded your firmware to 3.1.3!