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Mirrors > Home > ILE Home > Th. List > neli | GIF version |
Description: Inference associated with df-nel 2404. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
neli.1 | ⊢ 𝐴 ∉ 𝐵 |
Ref | Expression |
---|---|
neli | ⊢ ¬ 𝐴 ∈ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neli.1 | . 2 ⊢ 𝐴 ∉ 𝐵 | |
2 | df-nel 2404 | . 2 ⊢ (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) | |
3 | 1, 2 | mpbi 144 | 1 ⊢ ¬ 𝐴 ∈ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 1480 ∉ wnel 2403 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 df-nel 2404 |
This theorem is referenced by: renepnf 7813 renemnf 7814 nn0nepnf 9048 xrltnr 9566 pnfnlt 9573 nltmnf 9574 inftonninf 10214 topnex 12255 |
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