Notation of a point on a plane

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I'm having trouble finding the correct way to notate following conclusion about plane $H$ and point $A$. ($A \in H$)

If plane $H$ is not parallel to the $yz$-plane of the coordinate system, a $A_x$ exist for every combination of $A_y$ and $A_z$

My try

$$\forall H \nparallel H_{yz}, A_x \exists \forall A_y, A_z \in \Bbb R $$