Definition df-id 5488

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28805). (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 5487	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1963	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5135	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1538	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5489  dfid2  5490  dfid3  5491  reli  5736  ideqg  5761  opabresid  5958  opabresidOLD  5960  cnvi  6048  dffun2OLD  6446  fsplit  7964  ider  8541  epinid0  9366  bj-dfid2ALT  35243  bj-opelidb  35330  bj-ideqgALT  35336  bj-idreseq  35340  bj-idreseqb  35341  bj-ideqg1  35342  bj-ideqg1ALT  35343  cossssid2  36591  cossid  36603