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

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 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.