Definition df-id 5545

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 31035). (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 5544	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1994	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5166	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1569	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is used by:  dfid4  5546  dfid2  5547  dfid3  5548  reli  5803  ideqg  5828  cnvi  5862  opabresid  6041  fsplit  8128  ider  8755  epinid0  9599  bj-dfid2ALT  38022  bj-opelidb  38116  bj-ideqgALT  38122  bj-idreseq  38126  bj-idreseqb  38127  bj-ideqg1  38128  bj-ideqg1ALT  38129  cossssid2  39533  cossid  39545