Description: Weak ordering property of ordinal exponentiation. (Contributed by NM, 6-Jan-2005) (Revised by Mario Carneiro, 24-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | oeword | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oeord | |
|
2 | oecan | |
|
3 | 2 | 3coml | |
4 | 3 | bicomd | |
5 | 1 4 | orbi12d | |
6 | onsseleq | |
|
7 | 6 | 3adant3 | |
8 | eldifi | |
|
9 | id | |
|
10 | oecl | |
|
11 | oecl | |
|
12 | 10 11 | anim12dan | |
13 | onsseleq | |
|
14 | 12 13 | syl | |
15 | 8 9 14 | syl2anr | |
16 | 15 | 3impa | |
17 | 5 7 16 | 3bitr4d | |