Description: An alternate definition of a limit ordinal, which is any ordinal that is neither zero nor a successor. (Contributed by NM, 1-Nov-2004) (Proof shortened by Andrew Salmon, 27-Aug-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | dflim3 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lim | |
|
2 | 3anass | |
|
3 | df-ne | |
|
4 | 3 | a1i | |
5 | orduninsuc | |
|
6 | 4 5 | anbi12d | |
7 | ioran | |
|
8 | 6 7 | bitr4di | |
9 | 8 | pm5.32i | |
10 | 1 2 9 | 3bitri | |