Theorem elnel

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

	Ref	Expression
Assertion	elnel	⊢ ( 𝐴 ∈ 𝐵 → 𝐵 ∉ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elnotel	⊢ ( 𝐴 ∈ 𝐵 → ¬ 𝐵 ∈ 𝐴 )
2		df-nel	⊢ ( 𝐵 ∉ 𝐴 ↔ ¬ 𝐵 ∈ 𝐴 )
3	1 2	sylibr	⊢ ( 𝐴 ∈ 𝐵 → 𝐵 ∉ 𝐴 )