Definition df-id 5517

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30458). (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 5516	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1963	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5158	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1541	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5518  dfid2  5519  dfid3  5520  reli  5773  ideqg  5798  opabresid  6007  cnvi  6097  fsplit  8057  ider  8670  epinid0  9506  bj-dfid2ALT  37209  bj-opelidb  37296  bj-ideqgALT  37302  bj-idreseq  37306  bj-idreseqb  37307  bj-ideqg1  37308  bj-ideqg1ALT  37309  cossssid2  38670  cossid  38682