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Mirrors > Home > ILE Home > Th. List > nelir | GIF version |
Description: Inference associated with df-nel 2443. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
nelir.1 | ⊢ ¬ 𝐴 ∈ 𝐵 |
Ref | Expression |
---|---|
nelir | ⊢ 𝐴 ∉ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nelir.1 | . 2 ⊢ ¬ 𝐴 ∈ 𝐵 | |
2 | df-nel 2443 | . 2 ⊢ (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) | |
3 | 1, 2 | mpbir 146 | 1 ⊢ 𝐴 ∉ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 2148 ∉ wnel 2442 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-nel 2443 |
This theorem is referenced by: prneli 3617 snnex 4448 ruv 4549 pnfnre 7998 mnfnre 7999 eirr 11785 sqrt2irr 12161 topnex 13556 |
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