/sci/ - Science & Math

I understand how it follows from ZFC that a set can't contain itself, however, I fail to find a reason to show that sets can't cyclically refer to one another, which seems paradoxical to me.
You see,
[eqn]
x_1 = \{ x_2\}
x_2 = \{x_0\}
x_0 = \{x_1\}
[/eqn]
assuming none of the three are equal, they seemingly satisfy all axioms, or do they?