| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > df-nel | Structured version Visualization version GIF version | ||
| Description: Define negated membership. (Contributed by NM, 7-Aug-1994.) |
| Ref | Expression |
|---|---|
| df-nel | ⊢ (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | cB | . . 3 class 𝐵 | |
| 3 | 1, 2 | wnel 3046 | . 2 wff 𝐴 ∉ 𝐵 |
| 4 | 1, 2 | wcel 2108 | . . 3 wff 𝐴 ∈ 𝐵 |
| 5 | 4 | wn 3 | . 2 wff ¬ 𝐴 ∈ 𝐵 |
| 6 | 3, 5 | wb 206 | 1 wff (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) |
| Copyright terms: Public domain | W3C validator |