Theorem disjcsn

Description: A class is disjoint from its singleton. A consequence of regularity. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Revised by BJ, 4-Apr-2019)

	Ref	Expression
Assertion	disjcsn	|- ( A i^i { A } ) = (/)

Proof

Step	Hyp	Ref	Expression
1		elirr	|- -. A e. A
2		disjsn	|- ( ( A i^i { A } ) = (/) <-> -. A e. A )
3	1 2	mpbir	|- ( A i^i { A } ) = (/)