Definition df-id 5593

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30466). (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 5592	. 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 5228	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1537	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5594  dfid2  5595  dfid3  5596  reli  5850  ideqg  5876  opabresid  6079  cnvi  6173  dffun2OLDOLD  6585  fsplit  8158  ider  8800  epinid0  9669  bj-dfid2ALT  37031  bj-opelidb  37118  bj-ideqgALT  37124  bj-idreseq  37128  bj-idreseqb  37129  bj-ideqg1  37130  bj-ideqg1ALT  37131  cossssid2  38424  cossid  38436