Is there a name for statements about set inclusion?

A statement like the following is called an equality: $$2 + 2 = 4$$

In contrast, a statement like the following is called an inequality:

$$2 + 2 < 5$$

One can refer to groups of these statements with phrases like "We list several important equalities below" or "Recall the inequality on the previous page".

Is there a name for statements like this, indicating inclusion in a set? $$x \in \mathbb{X}$$

Specifically, it would be nice to know if there is a name that can be used to refer to groups of these statements.

I considered "definition" but if one has defined the member of the set (say, $$x$$ from the previous example) is a different way already, and one wishes to express that $$x$$ is a member of some, also previously defined, set, then "definition" doesn't work. One could the generic term "lemma" or use "statement" as I have been in this question, but I'm curious if there is another, more specific term.

The question of whether there is a similar name for statements like this, indicating exclusion from a set arises naturally, as well:

$$y \notin \mathbb{X}$$

Maybe "membership" for $$x\in X$$.