Dear friend, a friend of mine is called 'double genitive' in English. It is formed by combining an of- construction with a genitive. It means, as you correctly suppose, 'one of my friends'.
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iiluvpsychodifference between "one of my friends" and "a friend of mine"The meaning is exactly the same.
Gleb_Chebrikoffmy friend - presupposes definiteness vs. a friend of mine - indefiniteness <it is not known which friend, just one of them>Depending on your explanation, I wonder that If the phrase the friend of hers