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Mirrors > Home > ILE Home > Th. List > df1o2 | 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 6395 | . 2 ⊢ 1o = suc ∅ | |
2 | suc0 4396 | . 2 ⊢ suc ∅ = {∅} | |
3 | 1, 2 | eqtri 2191 | 1 ⊢ 1o = {∅} |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 ∅c0 3414 {csn 3583 suc csuc 4350 1oc1o 6388 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-un 3125 df-nul 3415 df-suc 4356 df-1o 6395 |
This theorem is referenced by: df2o3 6409 df2o2 6410 1n0 6411 el1o 6416 dif1o 6417 ensn1 6774 en1 6777 map1 6790 xp1en 6801 exmidpw 6886 exmidpweq 6887 pw1fin 6888 pw1dc0el 6889 ss1o0el1o 6890 unfiexmid 6895 0ct 7084 exmidonfinlem 7170 exmidfodomrlemr 7179 exmidfodomrlemrALT 7180 pw1on 7203 pw1dom2 7204 pw1ne1 7206 sucpw1nel3 7210 fihashen1 10734 ss1oel2o 14026 pwle2 14031 pwf1oexmid 14032 sbthom 14058 |
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