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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 3049 | . 2 wff 𝐴 ∉ 𝐵 |
4 | 1, 2 | wcel 2106 | . . 3 wff 𝐴 ∈ 𝐵 |
5 | 4 | wn 3 | . 2 wff ¬ 𝐴 ∈ 𝐵 |
6 | 3, 5 | wb 205 | 1 wff (𝐴 ∉ 𝐵 ↔ ¬ 𝐴 ∈ 𝐵) |
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