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 ( 𝐴𝐵𝐴𝐵 )

Proof

Step Hyp Ref Expression
1 elirr ¬ 𝐵𝐵
2 nelelne ( ¬ 𝐵𝐵 → ( 𝐴𝐵𝐴𝐵 ) )
3 1 2 ax-mp ( 𝐴𝐵𝐴𝐵 )