Definition df-id 5542

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30968). (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 5541	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1995	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5166	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1570	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is used by:  dfid4  5543  dfid2  5544  dfid3  5545  reli  5800  ideqg  5825  cnvi  5859  opabresid  6040  fsplit  8111  ider  8733  epinid0  9577  bj-dfid2ALT  37900  bj-opelidb  37993  bj-ideqgALT  37999  bj-idreseq  38003  bj-idreseqb  38004  bj-ideqg1  38005  bj-ideqg1ALT  38006  cossssid2  39410  cossid  39422