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Definition df-id 5166
Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 27594). (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 5165 . 2 class I
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3weq 2032 . . 3 wff 𝑥 = 𝑦
54, 2, 3copab 4856 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
61, 5wceq 1624 1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  dfid3  5167  dfid4  5168  ideqg  5421  cnvi  5687  dffun2  6051  epinid0  8662  bj-elid  33388
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