Definition df-id 5515

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30492). (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 5514	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1964	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5136	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1542	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5516  dfid2  5517  dfid3  5518  reli  5771  ideqg  5795  opabresid  6004  cnvi  6094  fsplit  8056  ider  8670  epinid0  9508  bj-dfid2ALT  37360  bj-opelidb  37454  bj-ideqgALT  37460  bj-idreseq  37464  bj-idreseqb  37465  bj-ideqg1  37466  bj-ideqg1ALT  37467  cossssid2  38867  cossid  38879