Class is Not Element of Itself

From ProofWiki
Jump to navigation Jump to search


Let $A$ be a class.

Then $A$ is not an element of itself:

$A \notin A$



This page is beyond the scope of ZFC, and should not be used in anything other than the theory in which it resides.

If you see any proofs that link to this page, please insert this template at the top.

If you believe that the contents of this page can be reworked to allow ZFC, then you can discuss it at the talk page.

$A \in A$ would create a relational loop for the class membership sign.

By No Membership Loops, this is a contradiction.