Existential

Existential-adjective
1-concerned with or relating to existence, especially human existence
2-in the context of existentialism, involved in or vital to the shaping of an individual's self-chosen mode of existence and moral stance with respect to the rest of the world
3-governed by the existential quantifier and thus asserting the existence of something by saying that there is at least 1 object that possesses the properties specified

noun
a proposition governed by the existential quantifier