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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 5536 | . 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦} | |
2 | 1 | relopabiv 5781 | 1 ⊢ Rel I |
Colors of variables: wff setvar class |
Syntax hints: I cid 5535 Rel wrel 5643 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-v 3450 df-in 3922 df-ss 3932 df-opab 5173 df-id 5536 df-xp 5644 df-rel 5645 |
This theorem is referenced by: ideqg 5812 issetid 5815 iss 5994 intirr 6077 elid 6156 funi 6538 f1ovi 6828 idssen 8944 symgcom2 31977 idsset 34504 bj-ideqgALT 35658 bj-ideqb 35659 bj-ideqg1ALT 35665 bj-opelidb1ALT 35666 bj-elid5 35669 brid 36796 iss2 36834 refrelid 37013 idsymrel 37052 disjALTVid 37246 |
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