Definition df-id 5533

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30363). (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 5532	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1962	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5169	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1540	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5534  dfid2  5535  dfid3  5536  reli  5789  ideqg  5815  opabresid  6021  cnvi  6114  dffun2OLDOLD  6523  fsplit  8096  ider  8708  epinid0  9553  bj-dfid2ALT  37053  bj-opelidb  37140  bj-ideqgALT  37146  bj-idreseq  37150  bj-idreseqb  37151  bj-ideqg1  37152  bj-ideqg1ALT  37153  cossssid2  38459  cossid  38471