ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-eprel GIF version

Definition df-eprel 4181
Description: Define the epsilon relation. Similar to Definition 6.22 of [TakeutiZaring] p. 30. The epsilon relation and set membership are the same, that is, (𝐴 E 𝐵𝐴𝐵) when 𝐵 is a set by epelg 4182. Thus, 5 E { 1 , 5 }. (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 4179 . 2 class E
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3wel 1466 . . 3 wff 𝑥𝑦
54, 2, 3copab 3958 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
61, 5wceq 1316 1 wff E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
Colors of variables: wff set class
This definition is referenced by:  epelg  4182  rele  4639
  Copyright terms: Public domain W3C validator