Is a husband's acknowledgment (Iqrar) of a dower (Mahr) equal to or less than the customary dower for his wife valid?

Primary text

The acknowledgment by a husband to his wife regarding a dower equal to or less than the customary dower for her is valid according to the consensus of the scholars. The evidence for this validity is that it is an acknowledgment of something whose cause is established, its existence is known, and no discharge from it is known, resembling the case where one acknowledges a debt proven by evidence but claims never to have paid it. This also applies if he purchases something from his heir and acknowledges the price to the heir, as the statement of the one receiving the acknowledgment is accepted regarding non-receipt of the price.