Is a woman's prayer valid if she prays in front of men with her face uncovered?

A woman covers her entire body during prayer except for her face. Regarding the uncovering of the hands, there is a difference of opinion: the majority of jurists hold that a woman prays with her face and hands uncovered, while some have gone to the extent of covering the hands. If she prays in the presence of non-mahram men, she is obliged to cover her face from them, even if she is in prayer. However, her prayer is valid even if she does not cover her face in their presence, because covering it is not for the sake of prayer, but for an external reason, which is to prevent the gaze of non-mahram men.