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 )