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Mirrors > Home > MPE Home > Th. List > df1o2 | Structured version Visualization version GIF version |
Description: Expanded value of the ordinal number 1. (Contributed by NM, 4-Nov-2002.) |
Ref | Expression |
---|---|
df1o2 | ⊢ 1o = {∅} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 8093 | . 2 ⊢ 1o = suc ∅ | |
2 | suc0 6259 | . 2 ⊢ suc ∅ = {∅} | |
3 | 1, 2 | eqtri 2844 | 1 ⊢ 1o = {∅} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∅c0 4290 {csn 4559 suc csuc 6187 1oc1o 8086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2793 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3497 df-dif 3938 df-un 3940 df-nul 4291 df-suc 6191 df-1o 8093 |
This theorem is referenced by: df2o3 8108 df2o2 8109 1n0 8110 el1o 8115 dif1o 8116 0we1 8122 oeeui 8218 map0e 8436 ensn1 8562 en1 8565 map1 8581 xp1en 8592 pwfi 8808 infxpenlem 9428 fseqenlem1 9439 dju1dif 9587 infdju1 9604 pwdju1 9605 infmap2 9629 cflim2 9674 pwxpndom2 10076 pwdjundom 10078 gchxpidm 10080 wuncval2 10158 tsk1 10175 hashen1 13721 sylow2alem2 18674 psr1baslem 20283 fvcoe1 20305 coe1f2 20307 coe1sfi 20311 coe1add 20362 coe1mul2lem1 20365 coe1mul2lem2 20366 coe1mul2 20367 coe1tm 20371 ply1coe 20394 evls1rhmlem 20414 evl1sca 20427 evl1var 20429 pf1mpf 20445 pf1ind 20448 mat0dimbas0 21005 mavmul0g 21092 hmph0 22333 tdeglem2 24584 deg1ldg 24615 deg1leb 24618 deg1val 24619 fply1 30859 bnj105 31894 bnj96 32037 bnj98 32039 bnj149 32047 rankeq1o 33530 ordcmp 33693 ssoninhaus 33694 onint1 33695 poimirlem28 34802 reheibor 35000 wopprc 39507 pwslnmlem0 39571 pwfi2f1o 39576 lincval0 44368 lco0 44380 linds0 44418 |
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