Definition df-id 5507

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28934). (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 5506	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1965	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5149	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1540	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5508  dfid2  5509  dfid3  5510  reli  5756  ideqg  5781  opabresid  5977  cnvi  6068  dffun2OLDOLD  6478  fsplit  8004  ider  8584  epinid0  9436  bj-dfid2ALT  35308  bj-opelidb  35395  bj-ideqgALT  35401  bj-idreseq  35405  bj-idreseqb  35406  bj-ideqg1  35407  bj-ideqg1ALT  35408  cossssid2  36702  cossid  36714