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Mirrors > Home > MPE Home > Th. List > df-eprel | Structured version Visualization version GIF version |
Description: Define the membership relation, or epsilon relation. Similar to Definition 6.22 of [TakeutiZaring] p. 30. The epsilon relation and set membership are the same, that is, (𝐴 E 𝐵 ↔ 𝐴 ∈ 𝐵) when 𝐵 is a set by epelg 5178. Thus, 5 E {1, 5} (ex-eprel 27599). (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
df-eprel | ⊢ E = {〈𝑥, 𝑦〉 ∣ 𝑥 ∈ 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cep 5176 | . 2 class E | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | vy | . . . 4 setvar 𝑦 | |
4 | 2, 3 | wel 2138 | . . 3 wff 𝑥 ∈ 𝑦 |
5 | 4, 2, 3 | copab 4862 | . 2 class {〈𝑥, 𝑦〉 ∣ 𝑥 ∈ 𝑦} |
6 | 1, 5 | wceq 1630 | 1 wff E = {〈𝑥, 𝑦〉 ∣ 𝑥 ∈ 𝑦} |
Colors of variables: wff setvar class |
This definition is referenced by: epelg 5178 rele 5404 epinid0 8668 cnvepnep 8674 dfnelbr2 41797 |
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