If the custom is for a girl not to marry her cousin, does he become a mahram for her?

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Check below answers in case you are looking for other related questions:
It is not correct to draw an analogy between donating blood and breastfeeding to prove that someone is a mahram
Maternal uncle marrying the daughter of his sister’s son

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It is not correct to draw an analogy between donating blood and breastfeeding to prove that someone is a mahram
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