[verb ない-form] + [noun] + は + ない [verb ない-form] + [noun (person/animal)] + は + いない [i-adj 〜い → 〜く] + ない + [noun] + は + ない
A noun with a ない-form in front of it, followed by はない, makes a double negative: "there is no X that doesn't…". The two negatives cancel into a strong "every": every day, everyone, everything, with no exception.
For people and animals the last verb is いない, for anything else ない. The noun takes は, since it is what the sentence denies exists.
These go beyond the plain present.
In polite speech the end becomes ありません or いません. For the past, it becomes なかった or いなかった.
~たことがない in front gives "there is no one who hasn't ever…".