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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 | dfid3 5054 | . 2 ⊢ I = {〈𝑥, 𝑦〉 ∣ 𝑥 = 𝑦} | |
2 | 1 | relopabi 5278 | 1 ⊢ Rel I |
Colors of variables: wff setvar class |
Syntax hints: I cid 5052 Rel wrel 5148 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1056 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-rab 2950 df-v 3233 df-dif 3610 df-un 3612 df-in 3614 df-ss 3621 df-nul 3949 df-if 4120 df-sn 4211 df-pr 4213 df-op 4217 df-opab 4746 df-id 5053 df-xp 5149 df-rel 5150 |
This theorem is referenced by: ideqg 5306 issetid 5309 iss 5482 intirr 5549 funi 5958 f1ovi 6213 idssen 8042 idsset 32122 bj-elid 33215 brid 34218 iss2 34252 refrelid 34411 |
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