Projection in Plane on Y-Axis along X-Axis

Theorem
Let $\pr_{Y, X}$ denote the projection on the $y$-axis along the $x$-axis:
 * $\forall P \in \R^2: \map {\pr_{Y, X} } P =$ the intersection of the $y$-axis with the line through $P$ parallel to the $x$-axis.

Let $P = \tuple {\lambda_1, \lambda_2}$ be an arbitrary point in $\R^2$.

Then:
 * $\map {\pr_{Y, X} } {\lambda_1, \lambda_2} = \tuple {0, \lambda_2}$