Freedom to live could also be summed up as living in the moment. Such as it is with the ending of Equilibrium. There is no hint of the future, nor is there any allusion to the past (besides the age of Libria being after a World War III sometime in our current future). There is only an expression of the enjoyment of freedom.
First, Preston destroys the propaganda machines. It is notable that he places some of the blood he spilled (that remains on him) on the image of Father before blasting the screen (symbolically sealing Father’s end), and then shooting all the other terminals from the propaganda center and emerging to another “T” shaped doorway to meet the mid-day sun.
Explosions fire in the distance, signaling the Resistance have fulfilled their mission as Jurgen promised: bombs detonated in each of the Prozium centers.
There is a cut to Robbie at Clerical school, Jurgen and the Resistance leaders at the incinerator, and Lisa (Preston’s daughter), who hear the noise of the blasts and each smile in turn. We see the dog that Preston rescued, licking Lisa’s hand.
Other Resistance members emerge from the Underground, killing Sweeps en masse.
The next scenes cut back to Preston surveying the scene, still clutching Mary O’Brien’s ribbon, and a smile slowly spreading across his face.