Step 1: Download the PS3.rar (from the link provided above) and extract the .pup file using WinRar.
Step 2: Put the PS3UPDAT.PUP onto the USB Flash Drive in the PS3/UPDATE/ folder.
Step 3: Power on your PS3 and navigate to the "System Update" option in the settings
Step 4: Choose "Update Via Media Storage"
Step 5: Let the PS3 search for the update, once it's found it it will ask you if you'd like to run it. Hit "OK"
Step 6: It should only take a few seconds, a message will pop up telling you what the lowest version firmware your PS3 can use!
Step 5: Congratulations! You're done!