Metamath Proof Explorer

Theorem neldifsn

Description: The class A is not in ( B \ { A } ) . (Contributed by David Moews, 1-May-2017)

Ref Expression
Assertion neldifsn 
|- -. A e. ( B \ { A } )

Proof

Step Hyp Ref Expression
1 neirr 
 |-  -. A =/= A
2 eldifsni 
 |-  ( A e. ( B \ { A } ) -> A =/= A )
3 1 2 mto 
 |-  -. A e. ( B \ { A } )