Metamath Proof Explorer


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