If due to the shortage of time for prayers one’s duty is to perform tayammum, but instead he performs wuḍūʾ with the intention of attaining proximity to Allah (qaṣd al‑qurbah), or [he performs wuḍūʾ] for a recommended act like reciting the Qur’an, then the wuḍūʾ he performed is valid [despite the fact that his duty was to perform tayammum].
Similarly, the wuḍūʾ would still be valid if he performed it with the intention of performing that prayer unless he did so without the intention of attaining proximity to Allah the Exalted. The sixth condition: one must perform wuḍūʾ with the intention of attaining proximity to Allah the Exalted, and it is sufficient to perform it with the intention of following the command of Allah the Exalted. If one performs wuḍūʾ to cool down or with some other intention, it is invalid.