I have been able to do this previously with a 5v Pro Mini, by simply connecting pins 11-13 (MOSI, MISO, and SCLK), Vcc, and GND on the Uno to the same pins on the Pro Mini, and pin 10 on the Uno to Reset on the Pro Mini. After loading the 'Arduino as ISP' sketch to my Uno, I can then load my required sketch via the Uno to the Pro Mini. All good (most of the time...). I know there is also another method - based on removing the actual ATMEGA chip from the Uno, but that relies on you having...
Can I use a 5v Arduino Uno as ISP to program 3.3v Pro Mini?
Can I use a 5v Arduino Uno as ISP to program 3.3v Pro Mini?