Definition df-id 5544

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30638). (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 5543	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1984	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5164	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1562	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5545  dfid2  5546  dfid3  5547  reli  5801  ideqg  5825  cnvi  5859  opabresid  6041  fsplit  8098  ider  8718  epinid0  9555  bj-dfid2ALT  37555  bj-opelidb  37649  bj-ideqgALT  37655  bj-idreseq  37659  bj-idreseqb  37660  bj-ideqg1  37661  bj-ideqg1ALT  37662  cossssid2  39062  cossid  39074