Definition df-id 5548

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30361). (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 5547	. 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 5181	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1540	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5549  dfid2  5550  dfid3  5551  reli  5805  ideqg  5831  opabresid  6037  cnvi  6130  dffun2OLDOLD  6542  fsplit  8114  ider  8754  epinid0  9612  bj-dfid2ALT  37029  bj-opelidb  37116  bj-ideqgALT  37122  bj-idreseq  37126  bj-idreseqb  37127  bj-ideqg1  37128  bj-ideqg1ALT  37129  cossssid2  38432  cossid  38444