Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-nelbr | Structured version Visualization version GIF version |
Description: Define negated membership as binary relation. Analogous to df-eprel 5029 (the epsilon relation). (Contributed by AV, 26-Dec-2021.) |
Ref | Expression |
---|---|
df-nelbr | ⊢ _∉ = {〈𝑥, 𝑦〉 ∣ ¬ 𝑥 ∈ 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnelbr 41288 | . 2 class _∉ | |
2 | vx | . . . . 5 setvar 𝑥 | |
3 | vy | . . . . 5 setvar 𝑦 | |
4 | 2, 3 | wel 1991 | . . . 4 wff 𝑥 ∈ 𝑦 |
5 | 4 | wn 3 | . . 3 wff ¬ 𝑥 ∈ 𝑦 |
6 | 5, 2, 3 | copab 4712 | . 2 class {〈𝑥, 𝑦〉 ∣ ¬ 𝑥 ∈ 𝑦} |
7 | 1, 6 | wceq 1483 | 1 wff _∉ = {〈𝑥, 𝑦〉 ∣ ¬ 𝑥 ∈ 𝑦} |
Colors of variables: wff setvar class |
This definition is referenced by: dfnelbr2 41290 nelbr 41291 nelbrim 41292 |
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