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| Description: Ordinal one is not equal to ordinal zero. |
| Ref | Expression |
|---|---|
| 1ne0 |
    |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0ex 2701 |
. . 3
  | |
| 2 | 1 | snnz 2449 |
. 2
 
|
| 3 | df1o2 4124 |
. . 3
 | |
| 4 | 3 | neeq1i 1584 |
. 2
 |
| 5 | 2, 4 | mpbir 190 |
1
|
| Colors of variables: wff set class |
| Syntax hints: wne 1577 c0 2270 csn 2399 c1o 4112 |
| This theorem is referenced by: xp01disj 4127 card1 4805 unxpdom2 4817 sucxpdom 4818 cdacomen 4901 1pi 4983 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 959 ax-gen 960 ax-8 961 ax-10 963 ax-11 964 ax-12 965 ax-14 967 ax-17 968 ax-4 970 ax-5o 972 ax-6o 975 ax-9o 1119 ax-10o 1136 ax-16 1206 ax-11o 1213 ax-ext 1452 ax-nul 2700 |
| This theorem depends on definitions: df-bi 147 df-or 224 df-an 225 df-ex 978 df-sb 1168 df-eu 1375 df-mo 1376 df-clab 1457 df-cleq 1462 df-clel 1465 df-ne 1579 df-v 1803 df-dif 2039 df-un 2040 df-nul 2271 df-sn 2402 df-pr 2403 df-suc 2944 df-1o 4117 |