Doubt on evaluation of limits using squeeze theorem /sandwich theorem

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Can we use sandwich theorem in the following situation :

If $$f(x)< g(x) \le h(x),$$

$$ \lim_{x \to a}f(x) = \lim_{x \to a}h(x) = p $$

Can one say $$\lim_{x \to a}g(x) = p$$ ??

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One can say that because if $a<b$ then surely $a\le b$.