Formula for the size of the union of neighbourhoods in a graph

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If $A,B \subseteq X$ and $|N(A)|=|A|$ and $|N(B)|=|B|$ in a finite bipartite graph $G$ with bipartition $X\cup Y$ then is it true that if Hall's condition holds on $X$ that:

$|N(A \cup B)|=|A \cup B|$ ?

It seems very obvious in my head, visually, but I don't know how to show it.