Description: A relationship between rank and R1 . See rankr1ag for the membership version. (Contributed by Mario Carneiro, 17-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | rankr1bg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r1funlim | |
|
2 | 1 | simpri | |
3 | limsuc | |
|
4 | 2 3 | ax-mp | |
5 | rankr1ag | |
|
6 | 4 5 | sylan2b | |
7 | r1sucg | |
|
8 | 7 | adantl | |
9 | 8 | eleq2d | |
10 | fvex | |
|
11 | 10 | elpw2 | |
12 | 9 11 | bitr2di | |
13 | rankon | |
|
14 | limord | |
|
15 | 2 14 | ax-mp | |
16 | ordelon | |
|
17 | 15 16 | mpan | |
18 | 17 | adantl | |
19 | onsssuc | |
|
20 | 13 18 19 | sylancr | |
21 | 6 12 20 | 3bitr4d | |