Metamath Proof Explorer


Definition df-id

Description: Define the identity relation. Definition 9.15 of Quine p. 64. For example, 5I 5 and -. 4 I 5 ( ex-id ). (Contributed by NM, 13-Aug-1995)

Ref Expression
Assertion df-id I = { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝑥 = 𝑦 }

Detailed syntax breakdown

Step Hyp Ref Expression
0 cid I
1 vx 𝑥
2 vy 𝑦
3 1 cv 𝑥
4 2 cv 𝑦
5 3 4 wceq 𝑥 = 𝑦
6 5 1 2 copab { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝑥 = 𝑦 }
7 0 6 wceq I = { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝑥 = 𝑦 }