Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nelir | GIF version |
Description: Inference associated with df-nel 2404. (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 2404 | . 2 ⊢ (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) | |
3 | 1, 2 | mpbir 145 | 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 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-nel 2404 |
This theorem is referenced by: prneli 3552 snnex 4369 ruv 4465 pnfnre 7807 mnfnre 7808 eirr 11485 sqrt2irr 11840 topnex 12255 |
Copyright terms: Public domain | W3C validator |