[hackandthink]

This makes sense in ZFC.

ZFC is a material set theory and is the most common set theory (and foundation).

It's different in a Structural Set Theory.

Michael Shulman: "Comparing material and structural set theories"

is really nice.

https://arxiv.org/abs/1808.05204

"In material set theories, the elements of a set X have an independent identity, apart from being collected together as the elements of X. Frequently, they are also sets themselves. These are also called “membership-based” set theories.

In structural set theories, the elements of a set X have no identity independentof X, and in particular are not sets themselves; they are merely abstract “elements” with which we build mathematical structures.