Is the statement "If so-and-so is cured, I will slaughter a sheep" considered a binding vow, or is a vow only valid with an explicit wording such as "I vow"?

A vow is an obligation undertaken by a responsible Muslim, as an act of devotion to Allah. It is valid by utterance, writing, or sign, and it does not have a specific formula; rather, it is valid with any statement that conveys commitment. The majority of scholars do not require the explicit utterance of the word "vow"; instead, it is valid with any formula that indicates commitment and obligation. However, if the formula lacks the word "vow," such as saying, "Upon me for Allah is such and such," the majority of jurists hold that it becomes binding and obligatory upon the one making the vow if they intended commitment thereby. The phrase mentioned in the question, "If so-and-so is cured, I will sacrifice a sheep," is considered a figurative expression. If its utterer intended it as a vow, then it is binding upon them; otherwise, it is not.