Prove that Newtons second law is the real law of motion

Proof. When we can show that Newton’s first and third law are contained in the second law, then we can say that it is the real law of motion.
(i) First law is contained in second law: According to Newton’s second law of motion,

It means that there will be no acceleration in the body if no external force is applied. This represents that a body at rest will remain at rest and a body in uniform motion will continue to move along the same straight line in the absence of an external force. This corresponds to Newton’s first law of motion. So, first law of motion is contained in Second law of motion