Theorem neli

Description: Inference associated with df-nel . (Contributed by BJ, 7-Jul-2018)

	Ref	Expression
Hypothesis	neli.1	⊢ 𝐴 ∉ 𝐵
Assertion	neli	⊢ ¬ 𝐴 ∈ 𝐵

Proof

Step	Hyp	Ref	Expression
1		neli.1	⊢ 𝐴 ∉ 𝐵
2		df-nel	⊢ ( 𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵 )
3	1 2	mpbi	⊢ ¬ 𝐴 ∈ 𝐵