Axiom of Limitation of Size implies Axiom of Union?

Question

On The Wikipedia page for Axiom of limitation of size it states that this axiom can be used to prove the axiom of union: https://en.wikipedia.org/wiki/Axiom_of_limitation_of_size

It implies the axiom schema of specification, axiom schema of replacement, axiom of global choice, and even, as noticed later by Azriel Levy, axiom of union[2] at one stroke.

I understand the first three axioms mentioned, but I haven't been able to find anything regarding the axiom of union. Does anyone know how this axiom implies the other? Thanks in advance.

Answer 1

Never mind, I did a little more searching and I finally found the information I was looking for. Sorry for the hassle. Here's where I found it: https://www.jstor.org/stable/2315201?seq=1#page_scan_tab_contents

Answer 2

Let $S$ be any set, and for each $s\in S$, take a nonempty set $s'$ such that there is no surjection $s\to s'$ (e.g., $s'=P(s)$). Then by König's theorem, there is no surjection $\bigcup S\to \prod_{s\in S} s'$. By limitation of size, this implies $\bigcup S$ cannot be a proper class, since any proper class surjects onto $V$ (and hence onto any nonempty class). That is, $\bigcup S$ is a set.