4 (10) Let \( f_n: \mathbb{R} \to \mathbb{R} \) be uniformly continuous and let \( f_n \) converge uniformly to \( f \). Prove that \( f \) is uniformly continuous.
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4 (10) Let \( f_n: \mathbb{R} \to \mathbb{R} \) be uniformly continuous and let \( f_n \) converge uniformly to \( f \). Prove that \( f \) is uniformly continuous.