Metamath Proof Explorer


Theorem elnotel

Description: A class cannot be an element of one of its elements. (Contributed by AV, 14-Jun-2022)

Ref Expression
Assertion elnotel ( 𝐴 ∈ 𝐵 → ¬ 𝐵 ∈ 𝐴 )

Proof

Step Hyp Ref Expression
1 en2lp ⊢ ¬ ( 𝐴 ∈ 𝐵 ∧ 𝐵 ∈ 𝐴 )
2 1 imnani ⊢ ( 𝐴 ∈ 𝐵 → ¬ 𝐵 ∈ 𝐴 )