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Definition df-eprel 5177
 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.)
Assertion
Ref Expression
df-eprel E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-eprel
StepHypRef Expression
1 cep 5176 . 2 class E
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3wel 2138 . . 3 wff 𝑥𝑦
54, 2, 3copab 4862 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
61, 5wceq 1630 1 wff E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
 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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