Definition df-id 5576

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30443). (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 5575	. 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 5203	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1540	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5577  dfid2  5578  dfid3  5579  reli  5834  ideqg  5860  opabresid  6066  cnvi  6159  dffun2OLDOLD  6571  fsplit  8138  ider  8778  epinid0  9636  bj-dfid2ALT  37059  bj-opelidb  37146  bj-ideqgALT  37152  bj-idreseq  37156  bj-idreseqb  37157  bj-ideqg1  37158  bj-ideqg1ALT  37159  cossssid2  38462  cossid  38474