Let G and H be two graphs. Prove that $\chi '(G \cup H) \leq \chi ' (G) + \chi ' (H)$.

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Let G and H be two graphs (not necessarily edge disjoint). Prove that $\chi '(G \cup H) \leq \chi ' (G) + \chi ' (H)$.

Here $\chi '$ represents the edge chromatic number. Not sure where to start with this really. Any help appreciated.