Theorem nelir

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

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

Proof

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