Proof:

Given: AB and CD are two lines.

To prove:

They intersect at one point or they do not intersect.

Proof:

Suppose the lines AB and CD intersect at two points P and Q.

This implies the line AB passes through the points P and Q.

Also the line CD passes through the points P and Q.

This implies there are two lines which pass through two distinct point P and Q. But we know that one and only one line can pass through two distinct points. This axiom contradicts out assumption that two distinct lines can have more than one point in common.

The lines AB and CD cannot pass through two distinct point P and Q.