The three types of negations in the texts and their levels

LEVEL 1: نفي الوجود Negating the existence, and this is the default. Example: لا خالق إلا الله "There is no creator except Allah" this constitutes negation of the existence of any creator besides Allāh, the Exalted. This is the negation intended here because this is the default and it is also in line with the reality (there is no other creator). But if it is not possible for the negation to carry this meaning as the thing being negated does actually exist, the negation would then refer to invalidity of a matter in the shar'iah LEVEL 2: نفي الصحة Negating the validity Example: لا صلاة بغير وضوء "There is no prayer without ablution." A person may pray without being in a state of purity, and so the prayer exists, but it is negated in terms of validity in the shar'iah (i.e. The prayer is invalid). If it is not possible to apply this meaning to the negation due to the presence of evidence preventing it, the negation would then refer to deficiency and incompleteness LEVEL 3: نفي الكمال Negating the completeness/perfection Example: لا صلاة بحضرة طعام ولا وهو يُدافعه الأخبثان "There is no prayer in the presence of food or while one is suppressing urine and feces." Here, it refers to negation of perfection, although some of the scholars have said that if a person is so preoccupied that he does not know what he is saying in his prayer, then his prayer is not valid in this case. In any case, these three levels should be noted by the student of knowledge. The default in negation is the negation of existence. If that is not possible and the thing exists, then it is refers to the negation of validity. If that is not possible and evidence has established validity, then it refers to negation of perfection. Thus, the ḥadith, لا صلاة لمنفردٍ خلف الصف "There is no prayer for an individual standing alone behind the row" falls under the second category, meaning its validity has been negated, so the prayer of an individual standing alone behind the row is not valid. Source: https://www.alathar.net/home/esound/index.php?op=codevi&coid=54967