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 B A B

Proof

Step Hyp Ref Expression
1 elirr ¬ B B
2 nelelne ¬ B B A B A B
3 1 2 ax-mp A B A B