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Definition df-eprel 5224
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 𝐵𝐴𝐵) when 𝐵 is a set (see epelg 5225). Thus, 5 E {1, 5} (ex-eprel 27617). (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 5223 . 2 class E
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3wel 2157 . . 3 wff 𝑥𝑦
54, 2, 3copab 4906 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
61, 5wceq 1637 1 wff E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  epelg  5225  rele  5452  epinid0  8740  cnvepnep  8746  dfnelbr2  41856
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