I am reading Fulton's book and I have reached the proof of Bezout's theorem which states that:
Theorem: If $F$ and $G$ are two projective plane curves of degrees $m$ and $n$ respectively and they have no common factor,then $\sum\limits_{p} I(p,F\cap G)=mn$.
The proof uses the following result:
Lemma: If $F$ and $G$ are two projective plane curves and they have no common factor,then they intersect at finitely many points only.
But although I have understood the proof of Bezout's theorem,the only problem is that I have assumed this lemma(as I could not give a proof).Some help will be appreciated.