Definition df-id 5574

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 29677). (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 5573	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1967	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5210	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1542	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5575  dfid2  5576  dfid3  5577  reli  5825  ideqg  5850  opabresid  6048  cnvi  6139  dffun2OLDOLD  6553  fsplit  8100  ider  8736  epinid0  9592  bj-dfid2ALT  35935  bj-opelidb  36022  bj-ideqgALT  36028  bj-idreseq  36032  bj-idreseqb  36033  bj-ideqg1  36034  bj-ideqg1ALT  36035  cossssid2  37327  cossid  37339