Is it possible to program an Arduino Pro Mini using an Arduino Uno R3?
Just hook up the pins (RX, TX, reset, Power, and Ground) to the corresponding pins on your Uno.

You may have to take the ATMega328 out of your Uno for this to work.

Keep in mind that you need to hook it up to the correct power pin! If your pro mini is running at 3.3v then you must hook it up to the 3.3 pin on your Uno.

Check out the ArduinoToBreadboard page for a bit more info. Scroll down to "Uploading Using an Arduino Board". Although it shows you how to program an Arduino on a breadboard, the wiring is the same.