Proof:[br]Consider two distinct lines [i]l[/i] and [i]l'. [/i]Projective Axiom 3 tells us that [i]l [/i]and [i]l' [/i]have at least one point, Q, in common. Now suppose there exists a second point, P, distinct from point Q and shared by [i]l[/i] and [i]l'. [/i]That is, we have two distinct points, P and Q, that have two lines, [i]l [/i]and [i]l', [/i]in common. This contradicts Projective Axiom 2. Thus, [i]l [/i]and [i]l'[/i] cannot have a second point in common. Therefore, [i]l[/i] and [i]l' [/i]only have one point in common. We can then conclude that any two distinct lines in a projective plane have exactly one point in common.