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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 6360 | . 2 ⊢ 1o = suc ∅ | |
2 | suc0 4371 | . 2 ⊢ suc ∅ = {∅} | |
3 | 1, 2 | eqtri 2178 | 1 ⊢ 1o = {∅} |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 ∅c0 3394 {csn 3560 suc csuc 4325 1oc1o 6353 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-un 3106 df-nul 3395 df-suc 4331 df-1o 6360 |
This theorem is referenced by: df2o3 6374 df2o2 6375 1n0 6376 el1o 6381 dif1o 6382 ensn1 6738 en1 6741 map1 6754 xp1en 6765 exmidpw 6850 exmidpweq 6851 pw1fin 6852 pw1dc0el 6853 ss1o0el1o 6854 unfiexmid 6859 0ct 7046 exmidonfinlem 7123 exmidfodomrlemr 7132 exmidfodomrlemrALT 7133 pw1on 7156 pw1dom2 7157 pw1ne1 7159 sucpw1nel3 7163 fihashen1 10668 ss1oel2o 13552 pwle2 13557 pwf1oexmid 13558 sbthom 13584 |
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