Definition df-id 5550

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 31062). (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 5549	. 2 class I
2		vx	. . . 4 setvar 𝑥
3		vy	. . . 4 setvar 𝑦
4	2, 3	weq 1997	. . 3 wff 𝑥 = 𝑦
5	4, 2, 3	copab 5170	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1570	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is used by:  dfid4  5551  dfid2  5552  dfid3  5553  reli  5809  ideqg  5834  cnvi  5869  opabresid  6053  fsplit  8152  ider  8780  epinid0  9623  bj-dfid2ALT  38170  bj-opelidb  38264  bj-ideqgALT  38270  bj-idreseq  38274  bj-idreseqb  38275  bj-ideqg1  38276  bj-ideqg1ALT  38277  cossssid2  39681  cossid  39693