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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 5576 | . 2 ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} | |
2 | 1 | relopabiv 5822 | 1 ⊢ Rel I |
Colors of variables: wff setvar class |
Syntax hints: I cid 5575 Rel wrel 5683 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3463 df-ss 3961 df-opab 5212 df-id 5576 df-xp 5684 df-rel 5685 |
This theorem is referenced by: ideqg 5854 issetid 5857 iss 6040 intirr 6125 elid 6205 funi 6586 f1ovi 6877 idssen 9018 symgcom2 32897 idsset 35614 bj-ideqgALT 36765 bj-ideqb 36766 bj-ideqg1ALT 36772 bj-opelidb1ALT 36773 bj-elid5 36776 brid 37905 iss2 37943 refrelid 38121 idsymrel 38160 disjALTVid 38354 |
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