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Definition df-eprel 5433
 Description: Define the membership relation (also called "epsilon relation" since it is sometimes denoted by the lowercase Greek letter "epsilon"). Similar to Definition 6.22 of [TakeutiZaring] p. 30. The membership relation and the membership predicate agree, that is, (𝐴 E 𝐵 ↔ 𝐴 ∈ 𝐵), when 𝐵 is a set (see epelg 5434). Thus, ⊢ 5 E {1, 5} (ex-eprel 28221). (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 5432 . 2 class E
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3wel 2113 . . 3 wff 𝑥𝑦
54, 2, 3copab 5095 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
61, 5wceq 1538 1 wff E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
 Colors of variables: wff setvar class This definition is referenced by:  epelg  5434  epelgOLD  5435  rele  5667  epinid0  9052  cnvepnep  9059  bj-epelg  34479  dfnelbr2  43816
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