Metamath Proof Explorer


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 A =

Proof

Step Hyp Ref Expression
1 elirr ¬ A A
2 disjsn A A = ¬ A A
3 1 2 mpbir A A =