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Definition df-id 5580
Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30367). (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 5579 . 2 class I
2 vx . . . 4 setvar 𝑥
3 vy . . . 4 setvar 𝑦
42, 3weq 1959 . . 3 wff 𝑥 = 𝑦
54, 2, 3copab 5215 . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
61, 5wceq 1534 1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  dfid4  5581  dfid2  5582  dfid3  5583  reli  5832  ideqg  5858  opabresid  6059  cnvi  6153  dffun2OLDOLD  6566  fsplit  8131  ider  8771  epinid0  9643  bj-dfid2ALT  36772  bj-opelidb  36859  bj-ideqgALT  36865  bj-idreseq  36869  bj-idreseqb  36870  bj-ideqg1  36871  bj-ideqg1ALT  36872  cossssid2  38166  cossid  38178
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