Definition df-id 5556

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30751). (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 5555	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1990	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5172	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1568	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5557  dfid2  5558  dfid3  5559  reli  5813  ideqg  5837  cnvi  5871  opabresid  6052  fsplit  8111  ider  8731  epinid0  9566  bj-dfid2ALT  37645  bj-opelidb  37740  bj-ideqgALT  37746  bj-idreseq  37750  bj-idreseqb  37751  bj-ideqg1  37752  bj-ideqg1ALT  37753  cossssid2  39153  cossid  39165