Definition df-id 5480

Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 28699). (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 5479	. 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 5132	. 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
6	1, 5	wceq 1539	1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}

This definition is referenced by:  dfid4  5481  dfid2  5482  dfid3  5483  reli  5725  ideqg  5749  opabresid  5946  opabresidOLD  5948  cnvi  6034  dffun2  6428  fsplit  7928  ider  8492  epinid0  9289  bj-dfid2ALT  35163  bj-opelidb  35250  bj-ideqgALT  35256  bj-idreseq  35260  bj-idreseqb  35261  bj-ideqg1  35262  bj-ideqg1ALT  35263  cossssid2  36513  cossid  36525