He used a credit card, which is haraam, and he owes money. Should he pay it off?

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Check below answers in case you are looking for other related questions:
Is it permissible to take a loan from the government’s social fund?
Entering into a partnership with a person who deals with bribes and riba

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Related Answers:
Should he take a riba-based loan to get medical treatment for his son?
Writing a letter stating salary for someone who will use it to get a riba-based loan
The ruling on going for Hajj and ‘Umrah and paying by means of credit cards
Is it permissible to take a loan from the government’s social fund?
Entering into a partnership with a person who deals with bribes and riba

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