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| Mirrors > Home > MPE Home > Th. List > df-id | Structured version Visualization version GIF version | ||
| Description: Define the identity relation. Definition 9.15 of [Quine] p. 64. For example, 5 I 5 and ¬ 4 I 5 (ex-id 30443). (Contributed by NM, 13-Aug-1995.) |
| Ref | Expression |
|---|---|
| df-id | ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cid 5575 | . 2 class I | |
| 2 | vx | . . . 4 setvar 𝑥 | |
| 3 | vy | . . . 4 setvar 𝑦 | |
| 4 | 2, 3 | weq 1962 | . . 3 wff 𝑥 = 𝑦 |
| 5 | 4, 2, 3 | copab 5203 | . 2 class {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
| 6 | 1, 5 | wceq 1540 | 1 wff I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
| Colors of variables: wff setvar class |
| This definition is referenced by: dfid4 5577 dfid2 5578 dfid3 5579 reli 5834 ideqg 5860 opabresid 6066 cnvi 6159 dffun2OLDOLD 6571 fsplit 8138 ider 8778 epinid0 9636 bj-dfid2ALT 37059 bj-opelidb 37146 bj-ideqgALT 37152 bj-idreseq 37156 bj-idreseqb 37157 bj-ideqg1 37158 bj-ideqg1ALT 37159 cossssid2 38462 cossid 38474 |
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