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Mirrors > Home > ILE Home > Th. List > nelir | GIF version |
Description: Inference associated with df-nel 2436. (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 2436 | . 2 ⊢ (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) | |
3 | 1, 2 | mpbir 145 | 1 ⊢ 𝐴 ∉ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 2141 ∉ wnel 2435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-nel 2436 |
This theorem is referenced by: prneli 3608 snnex 4433 ruv 4534 pnfnre 7961 mnfnre 7962 eirr 11741 sqrt2irr 12116 topnex 12880 |
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