Law of conservation of momentum, Consider two bodies colliding. momentum before collision of the bodies be PI1, PI2 . after collision PF1, PF2.
Conservation of momentum PF2+PF1=PI1+PI2
expression on both sides are change in momentum., dP1, dP2
differentiate to obtain,
Force on 2 due to 1= - Force on 1 due to 2.
This proves Newtons third law of motion.