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

Step	Hyp	Ref	Expression
1		cid 5579	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1959	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5215	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1534	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

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