There's no need to prove it. It is one of the Euclid's postulates or axiom.
To prove = Lines l1 and l2 have only one point in common.
Proof =
suppose lines l1 and l2 intersect at two disticnt points say P and Q.Then l1 contains points P and Q.
Also, l2 contains points P and Q.
So two line sl1 and l2 pass through two distinct points P and Q.
But only one line can pass through two different points.   (axiom 3)
so the assumption we started with that two lines can pass through two disticnt point is wrong.
Hence, two lines cannot have more than one point in common.