Definition df-id 5455

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28517). (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 5454	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1971	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5115	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1543	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5456  dfid3  5457  reli  5696  ideqg  5720  opabresid  5917  opabresidOLD  5919  cnvi  6005  dffun2  6390  fsplit  7885  ider  8427  epinid0  9216  bj-opelidb  35058  bj-ideqgALT  35064  bj-idreseq  35068  bj-idreseqb  35069  bj-ideqg1  35070  bj-ideqg1ALT  35071  cossssid2  36323  cossid  36335