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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