Is forgiving a debt by stating 'I pardoned you for it' valid?

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It is valid to say, 'I pardoned you for it' ('Afawtu laka 'anhu). This is supported by the saying of God Almighty regarding the dower in a broken marriage contract: {unless they forgive or he in whose hand is the marriage knot forgives} (Quran 2:237), which is interpreted to mean forgiveness of the dower (Sadaq).