Definition df-id 5460

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28213). (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 5459	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1964	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5128	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1537	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5461  dfid3  5462  reli  5698  ideqg  5722  opabresid  5917  opabresidOLD  5919  cnvi  6000  dffun2  6365  fsplit  7812  ider  8325  epinid0  9064  bj-opelidb  34447  bj-ideqgALT  34453  bj-idreseq  34457  bj-idreseqb  34458  bj-ideqg1  34459  bj-ideqg1ALT  34460  cossssid2  35723  cossid  35735