Definition df-id 5576

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30257). (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 5575	. 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 5210	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1534	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5577  dfid2  5578  dfid3  5579  reli  5828  ideqg  5854  opabresid  6053  cnvi  6146  dffun2OLDOLD  6560  fsplit  8122  ider  8761  epinid0  9624  bj-dfid2ALT  36544  bj-opelidb  36631  bj-ideqgALT  36637  bj-idreseq  36641  bj-idreseqb  36642  bj-ideqg1  36643  bj-ideqg1ALT  36644  cossssid2  37940  cossid  37952