Is Phoenix a Chinese symbol?

Could you please clarify for me if Phoenix is indeed considered a symbol within Chinese culture? It's my understanding that the phoenix is a mythical bird often associated with rebirth and prosperity, but I'm not entirely sure if it holds a special significance or status as a symbol in Chinese tradition. If it does, could you elaborate on its symbolism and any cultural contexts in which it is particularly relevant? I'm genuinely curious to learn more about the cultural significance of the phoenix in China.