natural projection on a slice

Question

I'm currently studying Warner's book "Foundations of Differentiable Manifolds and Lie Groups". Within the proof of the Frobenius Theorem he is constructing a slice $S$ of a coordinate system $(V,y_1,\dotsc,y_d)$ on a $d$-manifold, where $S$ is given by $y_1=0$. He then says that we have a "natural projection in the $y$-coordinate system" $\pi: V\rightarrow S$. It's probably completely obvious but how is this map defined?

Thanks in advance!

Answer 1

$\pi(y_1,y_2,\dots,y_d) = (0,y_2,\dots,y_d)$