Definition df-id 5582

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30462). (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 5581	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1959	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5209	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1536	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5583  dfid2  5584  dfid3  5585  reli  5838  ideqg  5864  opabresid  6069  cnvi  6163  dffun2OLDOLD  6574  fsplit  8140  ider  8780  epinid0  9637  bj-dfid2ALT  37047  bj-opelidb  37134  bj-ideqgALT  37140  bj-idreseq  37144  bj-idreseqb  37145  bj-ideqg1  37146  bj-ideqg1ALT  37147  cossssid2  38449  cossid  38461