Description: A limit ordinal is equinumerous to its successor. (Contributed by NM, 30-Oct-2003)
Ref | Expression | ||
---|---|---|---|
Assertion | limensuc | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 | |
|
2 | id | |
|
3 | suceq | |
|
4 | 2 3 | breq12d | |
5 | 1 4 | imbi12d | |
6 | limeq | |
|
7 | limeq | |
|
8 | limon | |
|
9 | 6 7 8 | elimhyp | |
10 | 9 | limensuci | |
11 | 5 10 | dedth | |
12 | 11 | impcom | |