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Mirrors > Home > ILE Home > Th. List > reli | GIF version |
Description: The identity relation is a relation. Part of Exercise 4.12(p) of [Mendelson] p. 235. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.) |
Ref | Expression |
---|---|
reli | ⊢ Rel I |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-id 4173 | . 2 ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} | |
2 | 1 | relopabi 4623 | 1 ⊢ Rel I |
Colors of variables: wff set class |
Syntax hints: = wceq 1312 I cid 4168 Rel wrel 4502 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-opab 3948 df-id 4173 df-xp 4503 df-rel 4504 |
This theorem is referenced by: ideqg 4648 issetid 4651 iss 4821 intirr 4881 funi 5111 f1ovi 5360 idssen 6623 |
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