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Definition df-id 5454
Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28141). (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 5453 . 2 class I
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3weq 1955 . . 3 wff 𝑥 = 𝑦
54, 2, 3copab 5120 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
61, 5wceq 1528 1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  dfid4  5455  dfid3  5456  reli  5692  ideqg  5716  opabresid  5911  opabresidOLD  5913  cnvi  5994  dffun2  6359  fsplit  7803  ider  8315  epinid0  9053  bj-opelidb  34337  bj-ideqgALT  34343  bj-idreseq  34347  bj-idreseqb  34348  bj-ideqg1  34349  bj-ideqg1ALT  34350  cossssid2  35590  cossid  35602
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