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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 4290 | . 2 class I | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | vy | . . . 4 setvar 𝑦 | |
4 | 2, 3 | weq 1503 | . . 3 wff 𝑥 = 𝑦 |
5 | 4, 2, 3 | copab 4065 | . 2 class {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦} |
6 | 1, 5 | wceq 1353 | 1 wff I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦} |
Colors of variables: wff set class |
This definition is referenced by: reli 4758 ideqg 4780 opabresid 4962 cnvi 5035 dffun2 5228 ider 6570 cnmptid 13820 |
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