Lefschetz Hyperplane Theorem says: Let $X\subset\mathbb{C}P^n$ be a smooth projective variety of complex dimension $m$ and let $Y = X \cap H$ be a generic hyperplane section. Then the natural morphism $\pi_i(Y)\to \pi_i(X)$ is an isomophism for $i\le m-2$ and is onto for $i=m-1$.
Now $X\subset\mathbb{C}P^n$ be a simply connected smooth projective variety of complex dimension $m$ and $Y$ is the intersection of $X$ with hyperplanes s.t. $\dim Y=m-d$.
Then why does Lefschetz Hyperplane Theorem show that $Y$ is connected and simply connected if $\dim(Y) = \dim(X)-d = m-d\ge 2$?
I think it used the fundamental group of $X$ is trivial, however, how is that related to the dimension of $Y$ in Lefschetz Hyperplane Theorem?