MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-id Structured version   Visualization version   GIF version

Definition df-id 4953
Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 26683). (Contributed by NM, 13-Aug-1995.)
Assertion
Ref Expression
df-id I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-id
StepHypRef Expression
1 cid 4948 . 2 class I
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3weq 1861 . . 3 wff 𝑥 = 𝑦
54, 2, 3copab 4642 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
61, 5wceq 1475 1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  dfid3  4954  dfid4  4955  ideqg  5195  cnvi  5456  dffun2  5814  bj-elid  32262
  Copyright terms: Public domain W3C validator