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Mirrors > Home > ILE Home > Th. List > df-id | GIF version |
Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5. (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
df-id | ⊢ I = {〈x, y〉 ∣ x = y} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cid 4016 | . 2 class I | |
2 | vx | . . . 4 setvar x | |
3 | vy | . . . 4 setvar y | |
4 | 2, 3 | weq 1389 | . . 3 wff x = y |
5 | 4, 2, 3 | copab 3808 | . 2 class {〈x, y〉 ∣ x = y} |
6 | 1, 5 | wceq 1242 | 1 wff I = {〈x, y〉 ∣ x = y} |
Colors of variables: wff set class |
This definition is referenced by: reli 4408 ideqg 4430 opabresid 4602 cnvi 4671 dffun2 4855 ider 6075 |
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