Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 28517). (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
df-id | ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cid 5454 | . 2 class I | |
2 | vx | . . . 4 setvar 𝑥 | |
3 | vy | . . . 4 setvar 𝑦 | |
4 | 2, 3 | weq 1971 | . . 3 wff 𝑥 = 𝑦 |
5 | 4, 2, 3 | copab 5115 | . 2 class {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
6 | 1, 5 | wceq 1543 | 1 wff I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} |
Colors of variables: wff setvar class |
This definition is referenced by: dfid4 5456 dfid3 5457 reli 5696 ideqg 5720 opabresid 5917 opabresidOLD 5919 cnvi 6005 dffun2 6390 fsplit 7885 ider 8427 epinid0 9216 bj-opelidb 35058 bj-ideqgALT 35064 bj-idreseq 35068 bj-idreseqb 35069 bj-ideqg1 35070 bj-ideqg1ALT 35071 cossssid2 36323 cossid 36335 |
Copyright terms: Public domain | W3C validator |