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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 28141). (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
df-id | ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cid 5453 | . 2 class I | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | vy | . . . 4 setvar 𝑦 | |
4 | 2, 3 | weq 1955 | . . 3 wff 𝑥 = 𝑦 |
5 | 4, 2, 3 | copab 5120 | . 2 class {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
6 | 1, 5 | wceq 1528 | 1 wff I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
Colors of variables: wff setvar class |
This definition is referenced by: dfid4 5455 dfid3 5456 reli 5692 ideqg 5716 opabresid 5911 opabresidOLD 5913 cnvi 5994 dffun2 6359 fsplit 7803 ider 8315 epinid0 9053 bj-opelidb 34337 bj-ideqgALT 34343 bj-idreseq 34347 bj-idreseqb 34348 bj-ideqg1 34349 bj-ideqg1ALT 34350 cossssid2 35590 cossid 35602 |
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