Definition df-id 5565

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30182). (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 5564	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1958	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5201	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1533	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5566  dfid2  5567  dfid3  5568  reli  5817  ideqg  5842  opabresid  6040  cnvi  6132  dffun2OLDOLD  6546  fsplit  8098  ider  8736  epinid0  9592  bj-dfid2ALT  36447  bj-opelidb  36534  bj-ideqgALT  36540  bj-idreseq  36544  bj-idreseqb  36545  bj-ideqg1  36546  bj-ideqg1ALT  36547  cossssid2  37842  cossid  37854