Metamath Proof Explorer

Theorem elneq

Description: A class is not equal to any of its elements. (Contributed by AV, 14-Jun-2022)

Ref Expression
Assertion elneq 
|- ( A e. B -> A =/= B )

Proof

Step Hyp Ref Expression
1 elirr 
 |-  -. B e. B
2 nelelne 
 |-  ( -. B e. B -> ( A e. B -> A =/= B ) )
3 1 2 ax-mp 
 |-  ( A e. B -> A =/= B )