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| Mirrors > Home > MPE Home > Th. List > reli | Structured version Visualization version 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 5578 | . 2 ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} | |
| 2 | 1 | relopabiv 5830 | 1 ⊢ Rel I |
| Colors of variables: wff setvar class |
| Syntax hints: I cid 5577 Rel wrel 5690 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-ss 3968 df-opab 5206 df-id 5578 df-xp 5691 df-rel 5692 |
| This theorem is referenced by: ideqg 5862 issetid 5865 iss 6053 intirr 6138 elid 6219 funi 6598 f1ovi 6887 idssen 9037 symgcom2 33104 idsset 35891 bj-ideqgALT 37159 bj-ideqb 37160 bj-ideqg1ALT 37166 bj-opelidb1ALT 37167 bj-elid5 37170 brid 38307 iss2 38345 refrelid 38523 idsymrel 38562 disjALTVid 38756 |
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