Definition df-id 5554

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30900). (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 5553	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1995	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5171	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1570	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is used by:  dfid4  5555  dfid2  5556  dfid3  5557  reli  5811  ideqg  5835  cnvi  5869  opabresid  6050  fsplit  8117  ider  8737  epinid0  9580  bj-dfid2ALT  37796  bj-opelidb  37891  bj-ideqgALT  37897  bj-idreseq  37901  bj-idreseqb  37902  bj-ideqg1  37903  bj-ideqg1ALT  37904  cossssid2  39293  cossid  39305