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 } |