Given subset $A$ and $ A_x = \{y : (x,y) \in A\} $, Are the following equivalent

Question

(This is Baire-Fubini theorem for categories) For a subset $A \subset \mathbb R^2$ and $x \in \mathbb R$ we denote $$ A_x = \{y : (x,y) \in A\} $$

Are the following equivalent?

• $A$ is of first category.
• The set $\{x: A_x\space is \space not \space of \space first \space category\}$ is of first category.

I'm not sure how to show they're equivalent, any help would be appreciated.